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Dot Product - Mathematics for Engineers - Vectors - TU Delft - Duration: 7:49.
Hello!
Do you remember this situation from high school physics?
You were supposed to calculate "the work done" by a constant Force (F)
exerted on the car by moving it over a distance s.
At school you learned to take the product of the magnitudes of Force F,
distance s and the cosine of the angle between F and s.
This quantity is often written as F dot s and is called the dot product of Force and Displacement
if you regard Force and Displacement as vectors!
The big dot in the notation explains the name.
In this slide we used vector notation.
That's the reason that we wrote the magnitudes of the force and the displacement
of the previous slide as the lengths of the vectors F and s.
A disadvantage of calculating the dot product in this geometrical way is that you have to know
the angle between the vectors and the lengths.
Often however the components of the vectors are given and then the angle is hard to compute.
But If that's the case, I have good news:
then there is a much easier algebraic way to calculate the dot product!
Let's look how this works.
It is shown for two general three dimensional vectors a and b.
To calculate the dot product you just have to multiply the first components of the two vectors,
then the second ones and at last the third ones.
Adding the results gives the dot product.
With a little practice everyone can do it!
This is our formal definition of the dot product of two three dimensional vectors.
The dot product of two two dimensional vectors is defined in a similar fashion.
Here is a two-dimensional example:
Suppose the force F is the vector with components minus 4 and 3
and suppose you have moved the car over a distance of 3 meters.
Since the displacement is horizontal and in negative direction
you can describe this with a vector with components minus 3 and 0.
The work done is the dot product of the vectors F and s.
With our new formula you can simply calculate this dot product as the sum of the products
of the corresponding components.
In this example the answer is 12.
And now the three-dimensional case.
Suppose two vectors are given.
The dot product is then easily calculated,
again multiply the corresponding components
and add the results.
In this case the answer is minus 13.
In class I would let you think about the question that's on the slide now.
The dot product of a two and a three dimensional vector is asked for.
The answer is that it is not defined.
So remember:
only dot products of vectors with the same dimension can be calculated!
Before connecting the two different ways of calculating the dot product of two vectors,
one with a geometric approach and the other with an algebraic approach,
I will show you some nice properties to do meaningful calculations.
Let's have a look at these properties, valid for vectors of the same dimension.
The first states that the dot product is commutative,
a property well known from ordinary multiplication with numbers.
With numbers you are also used to the second property which combines the dot product with the sum,
better known as the distributive law.
The third property states the connection between dot product and scalar multiplication of vectors.
The fourth property, which is somewhat different, is easy to understand.
Think about it!
It states that the dot product of a vector and itself equals the square of its length.
A property that you are going to use often.
Especially the first three properties make you think that calculations with the dot product
are more or less the same as calculations with numbers.
But be careful!!
Some weird things can occur.
Curious?
Make the exercises!
One of these weird things is the fact that the dot product of three vectors isn't defined.
One reason for this is that the dot product of two vectors is a scalar.
The properties given here can all be checked by using the definition of the dot product.
Some of them are left to you as an exercise.
This example shows how you can use these properties to write the distance between two vectors
as a sum of dot products.
Useful since a geometrical approach is connected with an algebraic approach!
Using the fourth property you first write the square of the distance as a dot product.
Now using the first three properties you can rewrite the result as sum of dot products.
Now you of course want to know what the connection is between the geometric approach
this video is started with and the algebraic approach introduced a little later.
It appears to be a direct consequence of the well known Cosine Law which gives the connection
between the lengths of the three sides of a triangle and one of its angles.
Applying this law on the triangle formed by the common starting point and the two endpoints of two vectors,
you get the result as shown here in terms of lengths of vectors.
You can use the formula derived on the previous slide to rewrite the left hand side in terms of the dot product.
A little rewriting gives the connection searched for.
You may try to do it by yourself in the exercises.
All nice math,
but what else can be done with this concept!
Watch the next video to discover this!
But it's better to practice a little bit first.
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VLOG 8 // YOYOGI PARK + ASAKUSA + RAGE QUIT - Duration: 13:36.
We are at Meji Shrine
and it seems like here is a
flower competition
yeah a floral arrangement compatition
it looks really pretty
or maybe they make them randomly because they are bored today
But I think its a compatition
looks really pretty although flowers always look pretty
and there are priests lol
this man has a magic broom
which can fan the leafs out of the stones
and the leafs stay lying down .. aah the stones not the leafs
really creepy
we just take the leafs and put them on a heap
if I would do that all stones would be on a heap too
that cant be real
or he as a special education as a
leaf sweep guy
in a holy shrine
we just came out of the yoyogi park
and are on our way to the yoyogi station
but we didnt dismount here but in harajuku station
and we have no idea where the station is
but i guess somewhere here
beautiful
we got lost again
now we are on the right way
we always get lost as soon as we leave the house
thats so weird. we never go the right way
we found the yoyogi park cause its right next to harajuku station xD
all the other things we didnt foundat first attempt
the sushi we didnt found
for days
we just found it yesterday
but now we are on the way to the station
this time for sure
now we need to find the next spot
asakusa
I'm really agog if we will find it
we will see whole asakusa then
then we explore beautiful asakusa
i mean just remember the crepes store
we walked such a big detour
and we had just to walk left at the station
there arent many exits at suchs stations
maxmimun like 4 exits
maybe more at the big stations
normally there is north, west, east and south exit
and we always take the complete wrong exit on the opposite side
i dont know why
not even once luck
a huge building
really steep mountain
Nice we didnt found the station
theres no station
there is the station which means we need to go this way
ok
wrong way
always in the wrong directions. it was 50:50 chance
right or left and we went wrong again
how we do that
now we just need to wait
here is the list which shows you in which directions you need to drive
next is harajuku, shibuya ...
the ebisu, meguro ...
this is from the ginza line
it looks a little diffrent
but its basically the same
here are all
the stations by its names
itll change to romaji soon
there is it
not in english but you know
in that you can read it
now it shows all stations
there is the train information
when trains have delays (nearly never)
it also tells you what happend
its just the same. its written in hiragana, kanji and romaji
Basically all are build in the same way
we just arrived in asakusa (and found it)
and its extremly crowded
not as crowded as in ueno but still annoying
Especially I need to say that
nearly 40% forgeiners (just like me)
or maybe more
maybe many
asian forgeiners but you cant see that
you only can hear it
so it could be maybe 70% forgeiners
accordingly I feel a little
like as if me stuff would be stolen asap
and everyone is walking against my camera
we wanna go there
You need to throw 100Yen in here
you dont have to you can also be a stupid piece of shit
but we are cool and we want it to bring us luck
thats why we throw 100 yen in there
we are the rad bitches
soo i turn the camera like this
then you take this
then a rod should come out
thats the rod
and it is
san-juu ...
the you have to
thats the 3-10-7
you need to search it here
ok lets search for the 3
thats ours
the you put the rod back in
pull the drawer out
and the first slip of paper is yours
and the you know whats going on
I dont know exactly what I got
I gonna read it and tell you after
now we need to find a beautiful tree and i hold it in
this is quite to much to translate so I will write it again while I'm talkin german
there was a woman in the restaurant we ate in
she had three kids and two of them really freaked out
we were and still are pretty ashamed of the cause they were also germans
the younger child screamed the whole time and it was a really small restaurant
so the owner saw them the whole time....
they throw their food around and played with it ...
they acted really horrible and the mother didnt said a word
we really got mad but still didnt said a word
but we felt so bad the whole time because she cant educate her children
and maybe some people think that all germans are like this
and in germany there are some people who dont really educate their children anymore
they think that they should educate themselfs but you can see
what happens if children dont get any rules and are allowed to throw food around
we ride a rickshaw now
lisa wheedle me to
in the name of the rickshaw driver
but our rickshaw driver is quite handsome
so we can look at his sexy ass
hopefully he has a sexy ass
we get a roof
weird noise .. sorry XD
hopefully we wont say something like
"oh you weight too much"
he is so sporty
just in case you might wonder THIS IS GOOD ENGLISH
my coffee just arrived
and behind it is the street to the temple
its so beautiful
and my coffee in front of it
and lisa still waits for hers
we will eat our stuff now
with this amazing view
there the little cake
wait come I
ah ok
Is it a matcha cookie underneath it ?
oh yes they know whats good and its filled with whipped cream
oh lisa you love whipped cream dont you?
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Meet the Brother who Hiked without Limbs and Ended Up Converting our Fellowmen of the Sumadel Tribe - Duration: 23:48.
The province of Kalinga can be found in Region 14 of the Cordillera Administrative Region.
In the one hundred fifty barangays under its jurisdiction,
barangay Sumadel in the town of Tinglayan is the destination of our journey.
In this hilly barangay stands not only the new house of worship of the Church Of Christ,
but the faith of the brethren here also stands firm.
They are the brethren in the Church from the tribe of Sumadel.
From the Central Office of the Church Of Christ in Quezon City,
We traveled for almost 500 kilometers
Before reaching the district office of the province of Kalinga.
Which is equivalent to more or less 13 hours of travel time.
Along with some ministers and brethren
We started hiking up the mountains.
Right now, we're here at Barangay Bangad or the Tribe of Bangad,
and we need to leave our vehicles behind because the terrain is too difficult.
We would walk from here to Sumadel, it would take almost five hours
and the distance we will travel uphill is approximately eight to nine kilometers.
At present the place and the natives here are known
not only for the products from their harvests,
like brown rice and coffee;
the place is also popular for its arts and for their hospitality.
My tribe Sumadel is one of the most noted barangay and the most hospitable people,
the most respectful people, the most industrious people...
Sumadel has the lowest crime rate in the Tinglayan Municipality even in the barangay
because the people there have good relationship, they are very hospitable
you can stay there for free, and even the food and coffee are also free.
For the natives living in Sumadel, a few hours of walking is not a new thing.
It's not easy hiking up the mountain.
"If you fall, you're dead."
The path is slippery and narrow.
"That's what we still have to climb."
And if the hike downhill is hard, the hike uphill is even harder.
This path beside the mountain is the same path used by the ministers who first preached
about the Church Of Christ in this place.
The efforts of the early ministers in the District of Kalinga to spread the Gospel in Sumadel
went through severe hardships and difficulties,
because danger couldn't be avoided in their travels;
the path they treaded was very dangerous because the slightest mistake could cause them to fall off the cliff.
There was a minister who really fell off the cliff. He is brother Ernesto Dela Cruz.
Through the mercy and help of our Lord God
he is still with us and until now he still goes here even though the journey going up here is very dangerous.
The performance of ministers' duties here, their endurance and patience of the ministers, are clearly seen
especially the older ministers before.
Despite their local assignments and worship service assignments are very far, mountainous,
and the roads are difficult, they don't mind; they endure these conditions.
Because of the difficulty and danger of traveling to Sumadel
add to that the incidents of tribal wars,
which was why it was only in 1984 when the preaching of the Church began in this place,
and that was also the year when the local congregation was officially established,
the local congregation of Sumadel.
From here up to that house that you can see, we would walk and we would continue past that house
the tribe of Sumadel is still afar off from that house.
There's still an uphill climb
Before we reach the local congregation, we had to stop for a couple of times and rest.
Especially under these big trees near the river.
As we continued our journey,
we heard more stories from the ministers
and ministerial workers who were previously assigned in Sumadel
When one of the older ministers we were with in the district had a worship service assignment
I fetched him at Bangad local congregation because his vehicle could no longer make the climb.
Because the rain was too heavy, we reached this part. Before this part was wide enough
but due to the heavy rain, there was a landslide in this area and nothing was left
This path where we're standing was only repaired by the Sumadel tribe to walk on
From 4:00 a.m. we assembled at the district and until now we're still hiking
it has been hours of continued hiking.
The efforts of the men entrusted by the Church Administration
to be assigned here and preach the Gospel to the tribe of Sumadel cannot be discounted
They understand that their efforts would lead to further victories.
Meanwhile in Barangay Sumadel, Kalinga, the construction of the new house of worship of the Church Of Christ has begun
From Tabuk City, we would travel for more than 70 kilometers before reaching the place
where the materials would be dropped off
afterwards it would be manually lifted uphill to Barangay Sumadel.
A beautiful and orderly barangay chapel of the Church Of Christ
now stands in this mountain.
But who was God's primary instrument for establishing the Church Of Christ in these mountains?
Who was he who accompanied the ministers who first preached the words of God in this place?
He who first went up to the mountains to invite the people from the tribe of Sumadel?
It was in the 80s then
from Baguio City where he graduated from his studies,
he decided to return to the mountains
and be with the tribe of Sumadel.
He is Brother Samuel Abag-oy.
1977, I went to Baguio;
1979, I finished my studies;
and in 1981, I was baptized.
When I remembered my relatives in Sumadel, I also invited them to know the Church
So in 1988, they were baptized.
Before, there was no Church Of Christ or a member of the Church from the Sumadel tribe.
No one would have thought that through Brother Samuel,
the teachings of the Church would spread up to the top of this mountain.
The Church Of Christ began here when Brother Samuel Abag-oy came here
and began doing missionary works in this place.
Because of Brother Samuel Abag-oy,
many of his tribe members in Sumadel are now members of the Church Of Christ.
And on June 19, 2016,
the brethren conducted the first worship service in their new house of worship or barangay chapel.
When I found out that someone from INC Construction came over to the tribe of Sumadel,
I was overjoyed.
When it began,
the brethren had a hard time bringing the materials up here
for the brethren to have a place where they could worship.
As we were walking through the long path and as we were looking at Brother Samuel,
in his condition, we couldn't help but think about how, on many occasions,
he went up and down this mountain, alone,
to introduce to the tribe of Sumadel the Church Of Christ and the teachings upheld by its members.
We have proven that his intentions are truly genuine.
We are very fortunate that we have an inspiration like Brother Samuel
who bravely and patiently strove to propagate the words of our Lord God.
He did not look at his physical condition.
Instead, he was filled with compassion for his relatives here in the Sumadel tribe
so that they too could understand the doctrines of the Church Of Christ.
Seeing his condition and disability, you wouldn't believe that he was able to do that on his own,
that he strove to propagate the teaching with such diligence.
Though Brother Samuel had a hard time, due to the fact that he used his hands for walking,
he was really determined to invite people.
We are happy that he was able to invite us.
Even though they were still on the road until late in the evening,
this did not hinder them from bringing here the understanding of the importance of the Church Of Christ.
He needed to travel for four hours.
And though he had a hard time going up the mountain,
he pushed himself to do it, for he wants the people here to be saved.
If Brother Samuel was not a faithful believer and if he didn't have a high regard for duty,
he wouldn't have sacrificed to reach this place.
For Brother Samuel, he was able to do all these not because he was good or strong.
He succeed in the work of propagation because of the help and mercy of the Lord God.
That's why he is very thankful.
I'm thankful to God and I always pray that He would help me
so that I could invite more people because I want more people to be saved.
During the times when Brother Samuel had difficulties going up the mountain by himself,
especially when he wasn't feeling well,
using the little money he earned, he would hire people to carry him up,
so that he could reach the people whom he wanted to lead into the Church.
Back in 1984, we were the ones who carry Samuel Abag-oy.
Sometimes I would carry him but I wouldn't ask him to pay me.
My companions would be the ones given the payment of two pesos.
This was the tradition of Kalinga back then.
This was how diligent and dedicated Brother Samuel was
in obeying the commandment of the Lord God to propagate His words.
27 years had passed
since he last walked here using his hands.
It's only now that he once again saw the beauty of the mountains.
It's also only now that he would once again see his tribes people from Sumadel
who have been baptized inside the Church Of Christ for a long time now.
Only now, after 27 years.
I returned here to see the condition of our tribes people.
They are glad especially those whom I have invited.
The elders whom I invited before already passed away.
Their families, when I asked, are all active members of the Church,
even their children up to their grandchildren.
At last, we reached the site of the new house of worship.
We feel and see the joy of Brother Samuel.
From no one, there are now many members of the Church Of Christ.
From none, there is now an orderly and beautiful house of worship.
They are now able to perform the true worship and service to the Lord God.
In totality, Brother Samuel has already brought many people inside the Church.
They are the people whom he invited or encouraged
to examine and listen to the teachings upheld by the Church Of Christ.
He has been to many places where he also shared the teachings and do missionary works
and through the mercy and help of God, it's God's miracle,
many people were encouraged and became the pioneers of the local congregations there.
When I left Sumadel, I was able to have 48 people baptized in the Church.
When we transferred to the Local Congregation of Bangad, we were able to invite 26 people.
When we moved to Buagan, there were 18 that were baptized.
When we transferred to Bolo, we had 52.
Then we moved to Bayabat, 36 people were baptized.
When we transferred to Agbanaoag, we had 18 people baptized.
Since I was baptized back in 1981 until 2016, I was able to have 223 people baptized in the Church.
The following day before going down the mountains,
the ministers along with Brother Samuel bid the brethren in Sumadel goodbye.
They understand that it might be a long time before they see each other again and be in the company
of the man first used by the Lord God as an instrument for them to have the true hope in receiving salvation.
I am thankful to Brother Eduardo V. Manalo
because a house of worship was built for the brethren here.
I am greatly thankful to him so I hope that the Father in heaven always keeps him safe
for him to continue in administering the Church.
I am thankful to the Lord God because although this is my condition and at my age,
I strive to attend the worship services to be strengthened in my faith.
Whatever the difficulties may be as I walk using my hands,
especially at my age, my body always aches but the important thing is I am able to attend the worship services.
Anywhere that Brother Samuel's hands bring him,
those who are dear to him are sure that he brings with him his membership in the Church Of Christ.
They know that he will continue to propagate the faith that he received.
A solid proof of this is that Brother Samuel Abag-oy is proud to be a member of the Church Of Christ.
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Farming Simulator 17 VOGEL & NOOT HEROS 1000 Plow - Duration: 9:32.
HI GUYS !!!! Welcome to Farming Simulator 17 Mods Channel in this video I will show You a New Plow the VOGEL & NOOT HEROS 1000 Plow.
VOGEL & NOOT HEROS 1000 Plow 6m Working Width 17Km/h Working Speed Recommended Power 300Hp
To test the plow I will use the CLAAS AXION 900 Tractor 400+hp
At the first two passes the plow seems to not work properly But as you will see below this video the plow is fully functional
CLAAS Front Weight From Claas Xerion V5.0 Mod Check Description
If you enjoy watching my videos... Give thumb up SUBSCRIBE FOR MORE And for any question ( or just for say HI!!) LET comment I will be happy to answer you...... bb
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Dan Solin's Investing Secrets: Investing is Simple - Duration: 1:20.
Investing can be really simple.
For many investors, owning a target date fund from a low-cost provider like Vanguard
is the only investment you'll ever need.
Just pick the fund with a date closest to when you'll retire
Put all your savings into this fund.
Check your statement only once or twice a year.
Ignore the financial news! You're a long-term investor!
I told you investing is simple.
Until next time, I'm Dan Solin.
These videos are part of a movement to prevent you from becoming a victim of the securities industry.
We want you to be a smart investor!
Join us! Subscribe to these videos.
We'll keep them coming.
You can also get my investing insights by subscribing to my free weekly newsletter.
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How to Lose Belly Fat in 1 Week - Duration: 0:23.
How to Lose Belly Fat in 1 Week
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Prayer: An Intimate Conversation - Just a Minute! - June 28, 2017 - Duration: 1:01.
God is your heavenly Father.
And that changes everything about prayer.
First it makes your prayer more personal.
You're praying to someone you really know and to someone who really knows you.
So you don't have to be like those hypocrites who pray just to be noticed on to look more
spiritual.
You can simply share an intimate conversation with your heavenly Father.
And second, you know he cares about you.
He is interested in every detail of your life and already has his ear turned your way.
That means you don't have to beg and plead like the pagans do just to get him to listen.
He's so interested in you, he already knows what you need even before you ask him.
So when you pray, you are praying to One who loves and cares for you most.
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Apple testing system that controls iPhone alarms - Duration: 0:42.
READY TO HEAD TO BED WHEN YOU
DECIDE TO GRAB YOUR PHONE
BEFORE YOU SHUT YOUR EYES. NOW
APPLE SAYS THEY MIGHT BE
3
USING THE PHONE TO HELP YOU
SLEEP. THE COMPANY IS TESTING
A NEW SYSTEM THAT WOULD
AUTOMATICALLY CONTROL ALARMS
AND NOTIFICATIONS TO MANAGE
WHEN YOU SHOULD HEAD TO BED AT
NIGHT AND WAKE UP IN THE
MORNING.THE SLEEP TRACKER
WOULD USE SENSORS TO TRACK THE
GAP OF TIME BETWEEN WHEN YOU
GO TO BED AND THE ACTUAL
MOMENT WHEN YOU FALL ASLEEP.AN
ALARM WOULD BE SET UNLESS AN
ITEM IN YOUR CALENDAR TAKES
PRECEDENCE.
3
CLOSED CIRCUIT@AR@[
á]H@cABC Network@J[FDCLOSED CIRCUITúH@c á@AR@[ABC NetworkóH@cCLOSED CIRCUIT@J[FD áíH@cABC Network@AR@[CLOSED CIRCUIT]H@c á@J[FDABC NetworkúH@cCLOSED CIRCUIT@AR@[ áóH@cABC Network@J[FDCLOSED CIRCUITíH@c á@AR@[ABC Network]H@cCLOSED CIRCUIT@J[FD áúH@cABC Network@AR@[CLOSED CIRCUITóH@c á@J[FDABC NetworkíH@cCLOSED CIRCUIT@AR@[ á]H@cABC Network@J[FDCLOSED CIRCUITúH@c á@AR@[ABC NetworkóH@cCLOSED CIRCUIT@J[FD áíH@cABC Network@AR@[CLOSED CIRCUIT]H@c á@J[FDABC NetworkúH@cCLOSED CIRCUIT@AR@[ áóH@cABC Network@J[FDCLOSED CIRCUITíH@c á@AR@[ABC Network]H@cCLOSED CIRCUIT@J[FD áúH@cABC Networ
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Farming Simulator 17 CLAAS Axion 900 V 1.1.0.0 - Duration: 2:24.
HI GUYS !!!! Welcome to Farming Simulator 17 Mods Channel in this video I will show You a New Upgraded CLAAS Axion 900 Tractor.
CLAAS Axion 900 V 1.1.0.0 4 Engine Setup 4 Wheel Setup 2 Design Setup 3 Body Color 23 Rim Color
Changelog: - interactive control - cab suspension - dynamic hoses supported - passanger supported Author : Smety (CMT)
IC CONTROL SPACE
Auto turn on cabin light when doors is open Door And shock absorber sound CooL
If you enjoy watching my videos... Give thumb up SUBSCRIBE FOR MORE And for any question ( or just for say HI!!) LET comment I will be happy to answer you...... bb
-------------------------------------------
It's alright - Duration: 1:01.
I'm sorry
Are you okay?
I am now.
I'm sorry
We should go back.
I loved that girl.
It's always been you and me,
we belong to each other.
What killed him?
loyalty
Why do you wanna see Burrows so bad anyhow?
Just have a little faith.
Because he's my brother.
I love you,
I've got nothing.
I'm proud of you,
I'm proud of us.
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