the vector projection of v onto u is given by: proj[u]v = (u.v/u.u)*u

u.v = 3(-5) + 2(3) = -15 + 6 = -9

u.u = 3(3) + (2)(2) = 9 + 4 = 13

=> proj[u]v = (-9/13)<3,2> = <-27/13, -18/13>

you were correct!

the second is the same procedure, you just switch the vectors around.

see Vector Projection for more info