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Vectors and scalar Video Lecture - Class 9
FAQs on Vectors and scalar Video Lecture - Class 9
| 1. What are vectors and scalars? |  |
| 2. How are vectors represented? | |
Ans. Vectors can be represented using various methods. One common way is to use an arrow to denote the vector's direction and a line segment to represent its magnitude. The length of the arrow is proportional to the vector's magnitude, and the arrowhead indicates its direction. Vectors can also be represented using coordinate notation, where the vector's components are expressed as ordered pairs or triplets.
| 3. What operations can be performed on vectors? | |
Ans. Several operations can be performed on vectors, including addition, subtraction, scalar multiplication, and dot product. Vector addition involves combining two or more vectors to obtain a resultant vector. Vector subtraction is similar but involves subtracting one vector from another. Scalar multiplication scales the magnitude of a vector by a scalar value. The dot product is a mathematical operation that yields a scalar value and is used to determine the angle between two vectors.
| 4. How are vectors and scalars used in physics? | |
Ans. Vectors and scalars play a crucial role in physics, particularly in the field of mechanics. Vectors are used to represent physical quantities such as displacement, velocity, acceleration, and force, which all have both magnitude and direction. Scalars, on the other hand, are used to represent quantities like mass, temperature, time, and energy, which only have magnitude. By using vectors and scalars, physicists can accurately describe and analyze the motion and interactions of objects in the physical world.
| 5. Can vectors and scalars be converted into each other? | |
Ans. No, vectors and scalars cannot be directly converted into each other because they represent fundamentally different types of quantities. Vectors have both magnitude and direction, while scalars only have magnitude. However, in some cases, a scalar quantity can be derived from a vector quantity. For example, the magnitude of a velocity vector gives the speed, which is a scalar quantity. Similarly, the magnitude of a displacement vector gives the distance traveled, which is also a scalar quantity.
Text Transcript from Video
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.
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.
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Mar 01, 2025
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