Question

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

Answer 1

Divide u by its magntude
$$
\hat u={<-4,-3>\over \sqrt{4^2+3^2}}
$$

Answer 2

Does it always equal 1?

Answer 3

The magnitude of the new vector above will equal to 1:
$$
|\hat u|=1
$$

Answer 4

$$
|\vec u|=\sqrt{(-4)^2+(-3)^2}\\
\hat u={\vec u\over |\vec u|}=\left <{-4\over |\vec u|},{-3\over |\vec u|}\right >\\
|\hat u|=1
$$

Answer 5

Thank you, I wanted to make sure. Also could you help with another question?
Let u = <-5, -9>, v = <6, 8>. Find -8u - 2v.

Answer 6

Is it: (-8*-5 + -8*-9) - ( 2*6 + 2*8)?