Question

Precalc:
Let u = <-4, -3>
Find the unit vector in the direction of u, and write your answer in component form.

Answer 1

Here is our vector u.
Let's start by finding the `magnitude` or `length` of u.
Do you remember how to do that?

We have a triangle, so it's simply the length of the hypotenuse.

Answer 2

5

Answer 3

Ok good.\[\Large ||u||=5\]

Answer 4

To find the `unit vector` in the direction of u,
we take the vector u,
and divide each of it's components by `the length of u`.\[\Large \hat u\quad=\quad \frac{u}{||u||}\]

Answer 5

\[\Large \hat u\quad=\quad \frac{<-3,-4>}{5}\]Understand how that works?
We'll simply divide each component by 5.

Answer 6

(-4/5 , -3/5 )
this right?

Answer 7

Ah I wrote the 3 and the 4 backwards lol.

Yes good job! :)

Answer 8

thanx pal