Hello.
Welcome to the mini-course on vectors.
This course is meant for students who plan to win the Nobel prize.
It gives you all the basic knowledge you need to apply vector properties in Mechanics!
If you don't plan to win the Nobel prize, but you want to pass your exam in mechanics,
this course is also exactly what you need.
Take a look at this airplane!
It is surrounded by various arrows.
These arrows have a starting point, a direction and a length.
This picture of a bridge also shows such arrows.
These arrows are not drawn just to give the picture a scientific flavour.
They are very useful for making relevant computations.
In this video, we introduce the basic concepts of these arrows, called vectors in mathematics.
Vector is a latin word, which means carrier.
It was first used by 18th century astronomers investigating planet rotation around the Sun.
A vector is often used in geometry and physics to represent physical quantities
that have both magnitude and direction.
Think of physical quantities like speed, movement, acceleration and force!
Consider this pool table.
If you want to indicate a location on the pool table, this can be done by fixing an origin,
and a horizontal and vertical position of the location, relative to the origin O.
For example: the point (6,4) and the point (-8,2).
If we want to describe a movement on the pool table, this can be done using a vector.
The movement from (6,4) to (-8,2) can be represented by an arrow starting at (6,4) and ending at (-8,2).
If we want to...
If we denote the point (6,4) by A and (-8,2) by B,
the vector in this picture is denoted as AB with a little arrow on top.
There are various operations that can be applied to vectors.
In this video, we consider two of these: scalar multiplication and addition.
We start with addition.
These operations can be viewed from a geometric point of view as well as from an algebraic point of view.
We start with the geometric view.
So consider three points in the plane: A, B and C.
Construct the vectors AB and BC .
The sum of these is then obtained by following the two arrows, first AB and then BC.
This gives you AC .
Now, what to do if the two vectors are not nicely attached,
in the sense that head and tail of the two vectors are not connected?
Well, then it is important to realize that for vectors, only length and direction are important.
In that sense, the two vectors given here are actually equivalent.
When we look at a vector u or v, we have to stress that we mean vectors, rather than numbers.
Unfortunately, there is not just one universally accepted notation to do this.
Often, the u is underlined to stress that it is a vector and not a number.
Other people use u with a little arrow on top and other people use boldface.
In this video, we use the boldface notation.
Remember this is just a convention and don't panic when you see people using other ways
to indicate the difference between a scalar and a vector.
Ok. Now, since two vectors are considered equal whenever their length and direction coincide,
adding two vectors can be done by shifting the second vector such that its tail starts
at the head of the first vector.
In this picture, first shift the vector v such that its starting point is exactly the endpoint of u
and then add the vectors as before .
In practice however, if you want to add two vectors, usually you first shift their starting points to the origin.
Then the sum of the two vectors can be obtained by using the so called parallelogram law.
Vectors can also be multiplied by a number, often called scalar in this context.
Briefly, multiplying a vector by 3, means its direction is left unchanged
and its length is multiplied by this number 3.
For instance, consider this vector v.
3 times v is given by this.
Multiplying v by minus 3, on the other hand, will give a vector which has opposite direction to v,
and its length is still 3 times that of v.
Ok, let us now look at vector addition and scalar multiplication of vectors
from an algebraic point of view.
The standard algebraic representation of a vector in the two dimensional space,
is by its end point, assuming the vector starts at the origin.
The coordinates of the end point are stacked on top of each other
and collected between two tall brackets.
For instance (4,1) and (-3,5).
Using this representation, addition of two vectors is quite natural.
The numbers 4 and 1 are called components of the vector (4,1).
Geometrically, we see that u plus v starts at the origin and ends in (1,6) .
The representation of this sum vector is (1,6).
Note that the first component 1 of the sum vector u+v is simply the sum of the first components
4 and minus 3 of the vectors u and v.
Similarly, the second component 6 of the sum vector u+v is just the sum of the second components
1 and 5 of the vectors u and v.
Multiplying the vector u equals (4,1) by 2 gives (8,2), of course.
Multiplying u by minus a half, leads to (-2,-1/2).
This can be seen from the geometrical representation as well as from the algebraic representation.
The examples up till now were given in two dimensions.
In three dimensions, you can take exactly the same approach.
A vector has a direction and a length.
It can be represented by an arrow.
Here you see the vector u with end point (1, 2, 3).
Adding the vector (1, 2, 1), leads to the vector (2, 4, 4).
This can be seen by moving the second vector's tail to the first vector's head
and travelling along the connected arrows.
Alternatively, the sum of u and v can easily be obtained by adding just the components of the vectors.
In this video we defined vectors in two and three dimensional space
both geometrically by magnitude and direction, and algebraically by components.
You also learned how to apply the following operations:
addition of two vectors and multiplication of a vector with a scalar.
In the next video you will learn more about the length of a vector and distances between points.
Stay tuned!
For more infomation >> What is a vector? - Mathematics for Engineers - Vectors - TU Delft - Duration: 8:06.-------------------------------------------
Raw: Boy Faints Playing (The Floor is Lava) - Duration: 3:30.
This is a swindle uncle!
The ground can not be lava
Dislike
And a comment
Great clikbait
come on
Fran, Fran uncle!
Cheese, They are burning everyone
And your sister is raping her.
We come quickly there's something to do
My sister!
But as that everyone is burning
Yes it's christmas
It is impossible
Do not believe everything
But you have not seen all those people burning
is real
no , no, no
This people play creative
They are hackers
The hakers are killed by lava
You're stupid
But youtube trends say so
In the real world there are people burning
You have to believe me!
Everyone is burning
Look at the ground if you want to believe me
It really is true!
WTF.....
Camilo, what are you doing?
But as you are going to burn with the floor ¿this is normal?
Fool
You really must believe me
Look there are real images!
No wait aside...
Is 100% real
There is only one way to check it
Uncle, what are you going to do?
no
THE
STOP
FLOOR
do not do it!
IS
BITCH
LAVA........
no!
help
ahhhhh
Wait!
I'm black
♬HAPPY SONG♬
Wait
I'm not black
god!
ahhhhhh
-------------------------------------------
What is Orthogonal Projection? - Mathematics for Engineers - Vectors - TU Delft - Duration: 1:45.
Hi there!
Let's have another look at the moving car.
If you want to compute the force that causes the car to move forward, here is what you need to do.
Suppose the car is dragged along by a constant force F under an angle alpha.
The force F can be decomposed into two perpendicular forces:
a vertical force lifting the car,
and a horizontal one causing the car to move.
This horizontal force (minus the friction) is the force that actually makes the car move forward,
so we need to calculate the blue vector!
In a general setting the situation is as follows:
Given two vectors u and v, you want to find vectors u1 and u2,
such that u1 has the same direction as v,
u2 and v are orthogonal
and the sum of the blue vector and the yellow vector equals the green vector u.
The vector u1 is called the orthogonal projection of u onto v.
There is even a separate notation for it.
Imagine light shining from above onto u then u1 is in fact the shadow of u on v.
In the next video you will learn how to actually calculate orthogonal projections.
You should now do the following exercises to internalize the meaning of the concept just introduced.
This is really needed to understand the calculations done in the next video.
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5K Q&A - WHO IS 'LMAOBANGTAN' ?? - Duration: 6:37.
so apparently
5,000 of you decided
to subscribe to my channel..
nO but seriously
i am beyond,
bEYOND GRATEFUL
for all of you who susbcribed!
like back then i couldn't even think of
getting 100 subscribers!
surprisingly, people cared enough
to ask questions,
sooo let's get on with it
alright oH GOD
i'm just warning you in advance,
i'm a very, vERY BORING PERSON
in real life???
like i can hear some of you
already snoring to this video :')
well isNT THIS OFF TO A GOOD START
well visually, it's
young forever
and you never walk alone,
ESPECIALLY NOT TODAY'S CONCEPT
but if it's music-wise it's
gOT TO BE Dark&Wild and Skool Luv Affair,
those two albums bETTER GET MORE APPRECIATION
I S2G
i'm younger than 18 and
i'm asian, hence i live in asia obv
so have fun guessing!!1!
well my name's Aretha,
i'm not gonna tell you
my full name, cuz thats a lil creepy
okay so long story short
i wasnt planning to start a channel at all??
at first i was just forced
to use youtube to show my friend
this bangtan FMV i made
it was this one
but since the file was too large
to send through the chat,
i had to create a YT channel and like
post (show it) it from there
but somehow it got views?????
and so i started making more videos,
because I *was bored and it *was summer break
so I kept making more videos and
people seem to like *them
and now we're here! :D
uH who even HAS biases these days??./?/
having a bias in bangtan is like
yOU CANT POSSIBLY CHOOSE ONE
HOW INSANE CAN YOU BE TO
CHOOSE JUST ONE???
for me at first it was Taehyung,
then it was Jimin,
then it's yoongi
and then its ALL OVER THE PLACE
and I kept switching lanes every week or every 5 minutes???
and after a while i just stopped knowing
uh so I use Final Cut Pro,
mine glitches a lot apparently
and its quite hellish to use from time to time
but yeah thats what i use
by the way ramenai I love your videos
and i am sincerely concerned for you okbye
I don't wake up early enough
to be called a morning person,
but I don't sleep THAT
late enough to be called a night owl???
i'm just lazy i guess
I love bangtan SO MUCH
to the point that
I will pay EACH of the members to
to step on my face
I mean i guess I ship all of them
with each other
because they're so supportive and so adorable
with each other, and it just warms my heart :")
and when it comes to bangtan with
girls or girl group members,
I don't really have a specific ship
that I support in mind,
I don't really care. As long as
they're happy I'm fine :3
I still love O!RUL82? era,
especially it's music and stuff,
I just like this one the least
out of all the eras ok
pls dont attack me
I mean it used to be 'jungshook' for me
but now it's just overused
so I don't really know anymore..
a year now :>
the EXACT vlive that
gave birth to :
all of Eat Jin,
and all of Namjoon's vlives!
for me, it's GOT to be
'haruman' / 'just one day'
this will FOREVER stay unbothered to me
that song was such a masterpiece
and can you believe yoongi wrote that
while he's recovering from his surgery????
for BTS, I was
sUUUper into 'Haikyuu!!'
which is this super gay anime
about guys who play with balls and stuff
I looked them (bts) up,
and I watched their music videos,
and everything just went downhill from there
uh I knew BIGBANG growing up,
and there was also PSY??
aaand newly-debuted EXO
was my guilty pleasure :"
I love groups like seventeen,
EXO,
NCT,
GOT7,
Mamamoo,
Monsta X,
AKMU,
iKON,
blackpink,
shinee, just so many others
but I can't just mention them all
in this one video
those are all the questions!
thank you so SO much for the questions
but I want to thank you guys
especially for all the support and love
you have given to me and my content!
I TRULY enjoy making videos
and I will continue to do so!
I'm very, vERY grATEFUL for
all of you
whether you've been here since
my first video,
or if you just got here,
thank you!!
so much <3
i'm not crying i'm not crying i'm not cryi
i'm a nobody honestly!
I don't deserve such nice comments,
you guys always cheered me up
with such nice comments ;-;
or comments like... these
um bUT EITHER WAY! thank you so much for the support!
-------------------------------------------
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.
-------------------------------------------
Why using YouTube correctly is so important. - Duration: 1:55.
We've all heard of YouTube.
But how many of us are using it correctly?
The difference between doing it right and doing it wrong
can mean a loss of thousands of views.
Let me give you an example.
So here's the example I promised you.
This is the same video.
It's a video we made for Lyn Creasey she give us gave me permission
to use this as an example.
And this video was uploaded by someone for her in June 2014.
So three years ago.
And basically in that time it's at 80 views.
Now in 2015 April 2015 we uploaded it to our Business Channel
which is a channel we run for our clients and stuff
and basically you can see that in two years
there's been 2,297 views
So basically there's a massive difference.
But more importantly if we go into the statistics of each of these
you'll see here, I'll bring it up to the center,
that
the video on Lyn's channels
have zero subscriptions to them
it does have one share.
If we do the same here
for
The Business Channel
you'll see that basically we've got five
subscriptions driven to the channel
and nine shares on this video.
So you can see there's a massive massive difference
between doing it right and doing it wrong.
So as you can see the difference is amazing.
That's why we put together our YouTube courses.
To help you better understand how YouTube works.
Which will lead to more effective results from your videos.
Call us today to find out more
and secure a place on one of our courses.
Alternatively simply click on the link below
-------------------------------------------
Is it easy to get your kids active? KCC Change4Life Families - Duration: 1:37.
For more infomation >> Is it easy to get your kids active? KCC Change4Life Families - Duration: 1:37. -------------------------------------------
Anti rambles about I Can't Understand What My Husband Is Saying - Duration: 2:01.
I have a new toy to play with...
shame I don't have any hands...
and a sex drive in general...
why have you done me on a female again?
Ah yes, cause you're a BUNCH OF FUCKING IMBECILES THAT'S WHY! *grumbling*
Oh well, might as well use this to make more content...
let's talk about Short Anime, then!
Why not?
Short enough to ramble about and there's a lot of short anime
that gets lost in the torrent of shit that is the modern anime industry.
And the first one I want to talk about is
I Don't Understand What in the name of Natalia Kobrynska`s Still Beating Heart My Husband Is Saying
Oh I'm going to have fun with this voice!
So this short anime tells us a story about the everyday life of Kaoru and Hajime
for all intents and purposes
a happy modern family that genuinely loves and cares for each-other,
even if, as the name of the show suggests,
they have some trouble in communicating with each-other, due to different backgrounds and hobbies.
Similar to other works of this author,
this is a comedy with a bit of romantic stuff, generally going into the cute territory,
but not over stretching it to the point where you'll die from hyperglycaemia.
The graphics are for the most part plain, but serviceable,
the music is for the most part the usual background noise, that you'll never remember, except for the endings
in the first season it is a cute little song about love
and the second one for some reason reminded me of Fallout.
So I think I can personally recommend this show to anyone who wants to have a bit of fun and maybe is married
as I can guarantee you that most of you will find a situation or two that you can very much relate
even if you're a European twat
...
with a female voice this sounds a lot less berating than it should...
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