# Thread: Orthogonal Projections

1. ## Orthogonal Projections

Find the orthogonal projection of the vector v onto the subspace W.

v= (-4, 5, -3)

W= span{(-3, 2, -1), (2, -3, -3)}

2. Originally Posted by My Little Pony
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 $w_1$ and $w_2$. Then the projection of v on W is $\langle v,w_1\rangle w_1 + \langle v,w_2\rangle w_2$.