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## Get ready for AP® Calculus

# Representing quantities with vectors

Vectors can represent real-world quantities where it's important to have both a magnitude and a direction. One example for that is force: you want to represent a force's magnitude (or strength), but it's also important to indicate in what direction the force is applied. Created by Sal Khan.

## Want to join the conversation?

- My question is about the physics of the example. The attraction force the magnet exert to pull the ball is in its own direction? Or it goes towards the ball, and the force that pulls the ball is the reaction force the ball exerts ?(1 vote)
- The force on the ball, by the magnet, would cause the ball to accelerate toward the magnet (absent other forces). So the corresponding force vector would point from the ball to the magnet.

The equal and opposite force on the magnet by the ball would then point from the magnet to the ball, and would accelerate the magnet toward the ball.(2 votes)

## Video transcript

- [Instructor] We're
told a powerful magnet is attracting a metal
ball on a flat surface. The magnet is pulling the ball at a force of 15 Newtons, and the magnet is 20 degrees to the south from the eastward direction
relative to the ball. Here are a few vectors where
the magnitude of vector A is equal to the magnitude of vector C is equal to 15 Newtons, and the magnitude of vector B is equal to the magnitude of vector D
which is equal to 20 Newtons. Which vectors can represent
the force of the team's pull? All right, pause this video and see if you can think about that on your own before we do it together. All right, now let's do it together. So before I even look at this, I'm just gonna look at the description. It has a magnitude of 15 Newtons. If we're talking about a force, you can view it as a
strength of 15 Newtons, and the magnet which
is pulling on the ball is 20 degrees to the south from the eastward direction
relative to the ball. So if this is the ball right over here, and if this is the eastward direction, it says that the magnet
is 20 degrees to the south from the eastward direction
relative to the ball. So the magnet would be in this direction, and this angle right
over here is 20 degrees, and the magnet is pulling on the ball, so the vector would go in that
direction towards the magnet, and we know it has a force of 15 Newtons, that's the magnitude. So it has to be a 15 Newton
magnitude right over here. So when we look at the choices, choice A is interesting, at least the direction looks right. It looks like it's 20
degrees south of due east, and they also tell us that the
magnitude of A is 15 Newtons. So I am liking A, now let's look at B. Well B looks 15 degrees south of due east, not 20 degrees south, so I will rule that out. And also B's magnitude is
wrong, it's 20 Newtons. C, the magnitude is
right, it's 15 Newtons, but the direction looks like
20 degrees north of due east. So I'll rule that one out. And last but not least, D, the direction is clearly wrong, it looks like 15 degrees
north of due east, and its magnitude is 20
Newtons, not 15 Newtons, so I'd rule that one out. Now to be clear a vector is only defined by its magnitude and its direction, not by its starting point. So if I had some other vector that looked like this right over here, that had the same magnitude and direction if this was right over
here, a 20 degree angle and it had a magnitude of 50 Newtons, then I would have
selected this one as well. You can shift a vector around like this as long as it has the same magnitude and it has the same direction, it is an equivalent vector.