30. find the vector v with the given magnitude and the same direction as u.
||v|| = 3
u = (4,-4)

The first thing you need to do is make a unit vector (a vector of length 1) that points in the direction of u, let's call it vector u'. To do this, simply divide u by its magnitude-- in other words, u' = u/||u||. 

||u|| = sqrt((4)^2 + (-4)^2) = sqrt(32) = 4*sqrt(2)

So, u' = <4,-4>/4*sqrt(2) = <1/sqrt(2),-1/sqrt(2)>

Since this vector has length one and points in the direction of u, we can just multiply it by 3 and we will have a vector of length 3. 

Thus, v = 3*u' = 3*<1/sqrt(2),-1/sqrt(2)> = <3/sqrt(2),-3/sqrt(2)> 


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