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Straightforward vector calc problem

  1. May 6, 2007 #1
    Studying for finals and I dont recall how to do projection and I don't like the explanation my textbook gives

    Problem: Find the distance from the point (1,3,-2) to the plane 2x + y - z = 1

    The answer to this problem should be sqrt(6)

    Relevant equations: ?

    The attempt at a solution:

    I know I have to do a projection of using two vectors, and I know one of the vectors is the normal vector to the plane (2i + j + k). I'm not sure how to find the other vector using the point given and which of the vectors is projected onto the other.
  2. jcsd
  3. May 6, 2007 #2


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    Staff Emeritus
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    Gold Member

    Welcome to the Forums,

    Well, what equation / method are you using to find the distance from the point to the plane?
  4. May 6, 2007 #3


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    Homework Helper

    draw a picture first....
    consider an arbitrary point P on the plane, let Q=(1,3,-2)
    now the magnitude of the proj of PQ in the direction of your normal vector IS the distance from Q to plane...
  5. May 7, 2007 #4
    ok, thanks. I got it now.
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