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How to find a vector that is perpendicular to every vector in a linear subspace?

  1. Apr 21, 2010 #1
    1. The problem statement, all variables and given/known data
    Hi, i dont know if you can help me but i am currently studying for my finals and i have come across a question which i am very confused about. i have looked it up in books but there seems to be no answer there. the question is Write down a vector of length 1 that is perpendicular to every vector in the linear subspace of r3 described by x-y+z=0. If you could help me i would be very greatful! thank you.
    I know that to find a normal vector which is perpendicular to another vector you use the cross product but i do not see how this will benefit me in this question as i am not given any vectors!
  2. jcsd
  3. Apr 21, 2010 #2


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    Homework Helper

    A first step would be to find out which subspace we're talking about, i.e. write down what form the vectors of this subspace take.
  4. Apr 21, 2010 #3


    Staff: Mentor

    The subspace is {<x, y, z> in R3 | x - y + z = 0}. What sort of a geometric object is this subspace?
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