Question

Let u = <-4, -3>. Find the unit vector in the direction of u, and write your answer in component form
Help me understand how to do this problem?

Answer 1

http://openstudy.com/users/jim_thompson5910#/updates/53b0bb9fe4b0a819ab150b5f

Answer 2

?

Answer 3

Looks like you and @gloves are in the same class?

Answer 4

He have a similar question?

Answer 5

We want to find \(c\) such that we multiply it by \(\mathbf u\) and have a vector magnitude 1.
In short: \(|c\mathbf u|=1\).\[
|c\mathbf u| = \sqrt{c\mathbf u \cdot c\mathbf u} = \sqrt{c^2(\mathbf u \cdot \mathbf u)} = c|\mathbf u| \implies c = \frac{1}{|\mathbf u|}
\]Therefore, the unit vector for \(\mathbf u\) is \(\mathbf u / |\mathbf u|\)

Answer 6

The reason why I did that, is because multiplying a vector by a scalar preserves direction, but not magnitude.

Answer 7

The unit vector has the same direction, but magnitude 1.

Answer 8

Ok so what number do I plug into that?

Answer 9

Well, \(\mathbf u = \langle -4,-3\rangle\)

Answer 10

Yeah so both -4 and -3?

Answer 11

These are the answers

Answer 12

First, do you know the dot product? \(\mathbf u \cdot \mathbf u\)?

Answer 13

No

Answer 14

Wait, really?

Answer 15

Wasn't in the lesson, the next lesson includes it

Answer 16

Okay. Do you know how to get the angle for \(\mathbf u\)?

Answer 17

No :(

Answer 18

wait i got it

Answer 19

I looked at this example

Answer 20

Yes, but you can't really use that if you don't know the dot product yet.

Answer 21

Wait, did you learn \(|\mathbf u|\)? That is how to find the magnitude of a vector?

Answer 22

yea

Answer 23

Ok.... Then you should have understood when I said \[
\frac{\mathbf u}{|\mathbf u|}
\]