Question

Find the vector v with the given magnitude and the same direction as u.

Magnitude: v=3 direction: u=(4,-4)

I am not sure what to do here or how to start.

Answer 1

Have you learned about unit vectors?

a unit vector (length = 1) in the same direction of
(a,b) = (a/√(a^2+b2) , b/√(a^2 + b^2))

so a unit vector along (4,-4) is (4/√32, -4/√32)

so one of length 3 is
3(4/√32, -4/√32)
= (12/√32, -12/√32)
which rationalizes to
(3√2/2 , -3√2/2)