Question

Can anyone help me answer this question?
Let u = <-4, -3>. Find the unit vector in the direction of u, and write your answer in component form.

Answer 1

do you know how to find the "length" or magnitude of the vector u ?

Answer 2

No

Answer 3

do you know how to do a "dot product" of u * u ?

Answer 4

yes

Answer 5

the magnitude of u is sqrt(u dot u)
first, what is u dot u = ?

Answer 6

I have no idea... I am confused

Answer 7

the dot product of two vectors <a,b> and <c,d> is a*c + b*d

Answer 8

if it is a vector dotted with itself, for example <a , b> dot <a, b> you get a*a + b*b

Answer 9

can you do
<-4, -3> dot <-4, -3 >
?

Answer 10

So 16+9=25?

Answer 11

yes
and the length of vector u is sqrt (u dot u)
so sqr(25)

Answer 12

sqr(25) simplifies

Answer 13

so 5

Answer 14

to make vector u "unit length", divide each of its "components" by the length of u
in other words divide -4 and -3 by 5

Answer 15

so it would be -4-3/5 right?

Answer 16

-4/5, -3/5

Answer 17

yes, and if you find the length of that vector you will find it is 1

sqrt( <-4/5, -3/5> dot < -4/5, -3/5> ) = sqrt( 16/25 + 9/25) = sqr( 25/25) = sqr(1) = 1

Answer 18

Thank you so much!!