Question

linear algebra: orthogonal complements

let W be the plane 3x+2y-z=0 in R3. Find a basis for W-perp.

answer: [-3; -2; 1]

Isn't the answer supposed to be [3; 2; -1] since it's perpendicular to the plane?

Answer 1

{-3,-2,1] and [3,2,-1] both span the same space, so they are two different ways of saying the same thing. Your answer, [3,2,-1] seems more natural, given that those are the coefficients of the plane.

Answer 2

How do I know if [-3, -2, 1] spans the same space? I thought you could check by plugging in the vector into the equation of the plane?

Answer 3

one way to see that {-3,-2,1] and [3,2,-1] span same space is to notice that they are paralel: [3,2,-1] = - {-3,-2,1]

Answer 4

just oposite directions

Answer 5

@he66666

Answer 6

Oh I see. Thanks myko!

Answer 7

yw