If u = 3i + 2j and v = -5i + 3j, find
1.)the vector projection of v onto u.
2.)the vector projection of u onto v.
for #1, is it < -27/13 , -18/13 >
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