Find the orthogonal projection of the vector v onto the subspace W.
v= (-4, 5, -3)
W= span{(-3, 2, -1), (2, -3, -3)}
Apply the Gram–Schmidt process to those two vectors in W, to get an orthonormal basis of W. Say it consists of the unit vectors $\displaystyle w_1$ and $\displaystyle w_2$. Then the projection of v on W is $\displaystyle \langle v,w_1\rangle w_1 + \langle v,w_2\rangle w_2$.