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

{W=

[x

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

z]

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- Apr 12th 2010, 11:15 AMnicolem1051Find 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] - Apr 12th 2010, 12:18 PMmaddas
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⊥?