SOLUTION: Determining an orthogonal basis for W = {(x, y, z); x

SOLUTION: Determining an orthogonal basis for W = {(x, y, z); x - 2y + z = 0}.

Question 892544: Determining an orthogonal basis for W = {(x, y, z); x - 2y + z = 0}.
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Choose any vector in W.
Set , then

If , then
(0,1,2)
.
.
.
Now use the dot product to find a perpendicular vector to this vector.

Let
then
Let , then
(1,-2,1)
.
.
.
Now take the cross product of those two vectors to find a mutually perpendicular vector to these two.
(0,1,2)X(1,-2,1)=(5,2,-1)
So then,
(0,1,2), (1,-2,1), and (5,2,-1) form an orthogonal basis of W.

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