# Thread: Find the orthogonal complement

1. ## Find the orthogonal complement

Find the orthogonal complement W⊥ of W and give the basis for W⊥.

{W=

[x
y ; x = t, y = -t, z = 3t}
z]

2. So you want the set of vectors orthogonal to (t,-t,3t). One vector orthogonal to this is (t,t,0). Another is the cross product of these two. Can you show that these two vectors span W⊥?