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Perpendicular distance from point to a plane

  1. Nov 6, 2011 #1
    1. The problem statement, all variables and given/known data
    Find the perpendicular distance from the point (1,2,3) to the plane x-2y-z=1
    One method: find the equation of the line throughout (1,2,3) perpendicular to the plane. Find the intersection of this line and the plane

    3. The attempt at a solution
    I know the vector (1,-2,-1) is a vector perpendicular to the plane
    I'm not sure how to find the distance between where the vector intersects the
    plane to the point.

    I know what to do if the vector was a line, but I am confused as to how to change the vector into a line.
  2. jcsd
  3. Nov 6, 2011 #2
    I think the line for the vector (1,-2,-1) that goes through P (1,2,3) is:
    x=1+t y=2-2t z=3-t

    Is this correct?
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