Question

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

Answer 1

you need to find
u/|u|

Answer 2

how do I do that?

Answer 3

is the absolute value of u <4, 3>?

Answer 4

find |u|

|u| = \( \sqrt{ u \cdot u} \)

so first find u dot u
can you do that ?

Answer 5

how exactly would I do that? just multiply u by u?

Answer 6

the "dot product" of a vector means
1) multiply "corresponding" elements
2) add up the products

example: < a,b> dot < c,d> = a*c + b*d

Answer 7

so what would be the c,d part? I only have a,b

Answer 8

you are doing c dot c

Answer 9

okay, so it'd be -4*-4+-3*-3?

Answer 10

yes

Answer 11

16+9=25 so sqrt(u dot u) is 5?

Answer 12

yes. that means the "length" of u is 5
or
|u| = 5
now divide u by 5 (each element of 5) to make it a "unit vector"

Answer 13

**
now divide u by 5 (each element of u by 5) to make it a "unit vector"

Answer 14

\[<\frac{ -4 }{ 5 },\frac{ -3 }{ 5 }>\]

Answer 15

@phi is that right?

Answer 16

yes, or < -0.8, -0.6>

notice if we find its length we get
\[ \sqrt{ -0.8\cdot -0.8 + -0.6\cdot -0.6 }= \sqrt{0.64+.36}= \sqrt{1}= 1 \]
the new vector has unit length (i.e. its length is one)