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## Precalculus

### Course: Precalculus > Unit 6

Lesson 1: Vectors introduction# Intro to vectors and scalars

AP.PHYS:

INT‑3.A (EU)

, INT‑3.A.1 (EK)

, INT‑3.A.1.1 (LO)

, INT‑3.A.1.2 (LO)

, INT‑3.A.1.3 (LO)

Scalars and vectors are two kinds of quantities that are used in physics and math. Scalars are quantities that only have magnitude (or size), while vectors have both magnitude and direction. Explore some examples of scalars and vectors, including distance, displacement, speed, and velocity. Created by Sal Khan.

## Want to join the conversation?

- Is it still a vector if we say "The brick moved 5m towards Sal" even if 'towards Sal' has no specified location.(682 votes)
- As you told towards Sal means you have given a specific direction as Sal is standing in a specific direction so it is a vector quantity(839 votes)

- Does vectors have a location in space? does it vary with time?

This is a question from my Physics textbook. I even couldn't understand the question. Can you explain and answer me?(228 votes)- A vector stores only two parameters of information - length and direction. It doesn't tell you anything about it's origin/location. It can vary with time if it's given as a function of time, for example if the vector symbolises speed of an accelerating object, then it does vary on time, if the speed is constant then it doesn't vary on time.(294 votes)

- What is the triangle symbol at4:30?(39 votes)
- The triangle is actually the symbol 'delta', which denotes 'change in'. So delta(t) means change in time.(117 votes)

- A scalar value cannot be a vector because it does no include direction, but can vectors be considered scalar?(21 votes)
- No, for the same reason. But the magnitude (modulus) of a vector is a scalar.(16 votes)

- What is the difference between distance and displacement?(12 votes)
- Distance is how far you go, displacement is how far you went relative to your starting position! Example: If I walk 2 miles from my house to the grocery store, and walk 2 miles back to my house, my distance traveled is four miles; however my displacement is zero because I'm back where I started.(56 votes)

- If people developed the ability to time-travel, would time be a vector or a scalar quantity?(13 votes)
- Being able to travel in a dimension doesn't determine if we use a scalar or vector quantity. The value July 20, 1969,20:17:40 UTC is a scalar time value but 35 minutes from now is a vector.(17 votes)

- O.K. so on earth we can say that an object is going with velocity v(direction North To South). But what I have learned now is that every point in the universe is the centre of universe.

so question 1

Is this true?

question 2

if yes than how will you define direction of a particle. I mean that everywhere you are going in the universe you are at the centre of it.(11 votes)- Deep questions!

1) Yes, that is a concept from relativity called reference frames. Einstein theorized that the laws of physics should all work no matter what object you think marks the center of the universe, and all experiments up to this point have agreed with him.

2) In a theoretical sense, the vectors you're seeing exist in Euclidean space, which does have a well-identified center (the origin). If someone is doing real-world problems, what you'll find is that they will (usually without mentioning it) assume that there is a standard frame of reference. For instance, if I want to talk about a person running around a circular track, I would assume that the origin is the spot where the person started running. In practice, you'll probably find that it isn't as confusing as you might fear.(20 votes)

- how is force a vector quantity?(7 votes)
- Force is a vector quantity. For e.g. when you apply force on a body in rest it comes in the motion in the direction of the force you applied.So it is a vector quantity(2 votes)

- Can a vector have zero component along a line and still have non zero magnitude?(6 votes)
- yes. when the vector is perpendicular to the line.(17 votes)

- What is the name for a quantity with only direction?(7 votes)
- It's not a quantity if it only has direction, right?

We have a name for it, though. It's called: direction.(7 votes)

## Video transcript

What I want to do
in this video is talk about the difference
between vectors and scalars. And they might sound like
very complicated ideas, but we'll see over the
course of the videos that they're actually
very simple ideas. So first I'll give you a
little bit of a definition. And then I'll give you
a bunch of examples, and I think the examples
will make things super clear. Hopefully, they'll make
things super clear. A vector is something
that has a magnitude, or you could kind of
view that as a size, and it has a direction. So "and" it has a direction. A scalar only has a
magnitude, or size. And if that doesn't
make sense to you, it will hopefully
make sense to you in a second when I
show you an example. For example. Let's say that I have,
let's say that that's the ground-- let me do
the ground in a more appropriate ground-like color. So this is green
right over here. And let's say that
I have a brick here. I have a brick on the ground. And I pick up that
brick, and I move it over to this place right over here. So I move the brick
right over there. And then I take a ruler
out, and I say, wow, I've moved the brick 5 meters. So my question to you, is
my measurement of 5 meters, is it a vector or a scalar? Well, if I just
tell you 5 meters, you just know the
size of the movement. You just know the
magnitude of the movement. So if someone were
to just say 5 meters, this is a scalar quantity. And when we're referring
to moving something, or how much something has, I
guess, changed its position, and I don't give
you the direction, we're talking about distance. And I'm assuming you've
heard the word distance. How far of a distance
has something traveled? So this is distance. So we could say that this
block, or this brick, because of my picking
it up and moving it, has moved a distance
of 5 meters. But if I didn't show
you this picture here, and someone just
told you that it moved a distance
of 5 meters, you wouldn't know if it moved
to the right 5 meters, you wouldn't know if it
moved to the left 5 meters, if it moved up or
down or in or out, or-- You don't know what
direction it moved 5 meters. You just know it moved 5 meters. If you want to
specify that, so, we could say that this
brick right over here, that it moved 5
meters to the left. Now we have specified a
magnitude, right over there. So that is a magnitude. And we have specified a
direction, to the left. So you now explicitly know that
they went 5 meters to the-- oh, sorry. It should be 5
meters to the right. Let me change that. So, 5 meters to the right
is what it got moved. It started here and went
5 meters to the right. So once again, the
magnitude is 5 meters, and the direction
is to the right. So what I've just
described to you right here is a vector quantity. So this, all of this
business right over here, this is a vector. And when you talk about
the movement, the change in position, and you give its
direction, the vector version of distance, I guess you could
call it, is displacement. So this right here
is displacement. So the correct thing
to say, you would say that this brick
has been displaced 5 meters to the
right, or it has been moved a distance of 5 meters. Distance is a scalar
quantity-- I didn't tell you what direction we moved it in. Displacement is a
vector quantity. We told you that
it is to the right. Now let's explore this if
we talk about the actual, well, we'll talk about the
speed or velocity of something. So let's say that this
5 meters was traveled and let's say that
the change in time-- let me just, because
you're probably not familiar with what that means. So let's say that the
change in time right here, when I moved this
block 5 meters, let's say that it
was, I don't know, let's say that the change
in time was 2 seconds. So maybe right when the
block started moving, maybe on my stopwatch it said 0. And then on my stopwatch
when it stopped moving, it said, or when it
got to this position, I should say-- when it
left from this position, my stopwatch said 0. When it got to this position
my stopwatch said 2 seconds. So the change in time, or the
duration we're dealing with, is 2 seconds. And this is, for all
we know, time only goes in the positive direction. So you could assume
that it's, you could pick that as a vector
or a scalar quantity, I guess, because there's
only one direction for time, as far as we know, or
at least in what we're going to deal with for
the simple physics. So what is a measure of
how fast this thing moved? So, how fast did
this thing move? So we could say it moved
5 meters in 2 seconds. Let me write this down. So it moved 5 meters
per 2 seconds. Or we could write this as
5/2 of a meter per second. Or 5 divided by 2 is what? 5 divided by 2 is 2.5
meters per second. This right here is just
the 5 divided by 2, let me make that clear. That right there is just
the 5 divided by the 2. So my question to you. This 2.5 meters per
second tells you how far it traveled in a
certain amount of time. Is this a vector or
a scalar quantity? It is telling you
how fast it went, but is it giving you just
a size of how fast it went? Or is it also giving
you direction? Well, I don't see
any direction here. So this is a scalar quantity. And the scalar quantity for
how fast something is going is speed. So we could say that
the speed of the brick is 2.5 meters per second. Now, if we do the
same calculation, and we say it went
5 meters-- I'll just write m for meters-- to the
right in 2 seconds, then what do we get? We get 2.5, once again, 2.5
meters per second-- I'll just abbreviate them as meters
per second-- to the right. So is this a vector
or a scalar quantity? I'm telling you the magnitude
of the speed, that's right here. This is the magnitude,
2.5 meters per second. And I'm also telling you
the direction, to the right. So this is a vector quantity. This is a vector quantity. And when you specify both
the speed and the direction, so the 2.5 meters per second
is a scalar, and the direction, you are talking about velocity. You are talking about velocity. So an easy way to
think about it, if you're thinking
about change in position and you specify the direction
of the change in position, you're talking
about displacement. If you're not talking
about the direction, you want the scalar version,
you're talking about distance. If you're talking about how
fast something is going, and you give the direction
that it's going in, you're talking about velocity. If you don't give the direction
you are talking about speed. Hopefully that helps
you a little bit. In the next video,
we're going start working with these a
little bit to start solving some basic questions
about how fast something is going, or how
far it might travel, or how long it might
take it to get someplace.