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Help : Perpendicular distance of the plane

  1. Oct 27, 2011 #1
    1. The problem statement, all variables and given/known data
    Find the perpendicular distance of the plane 5x+2y-z=-22 from the origin O by first finding the co-ordinates of the point P on the plane such that OP is perpendicular to the given plane.


    2. Relevant equations
    It only given plane vector,how i going to figure out the perpendicular distance?



    3. The attempt at a solution
    I really dont know where to start.Can help to elaborate?

    Thanks
     
  2. jcsd
  3. Oct 27, 2011 #2
    Set x and y equal to zero, solve for z. The perpendicular distance will be the absolute value of this number.
     
  4. Oct 28, 2011 #3

    You mean (X,Y.Z) = (0.0.Z)?Then minus the plane location?
     
  5. Oct 28, 2011 #4

    hotvette

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    Homework Helper

    One option is to use Lagrange Multipliers to get the coordinates of the point by treating it as a minimization problem (i.e. distance from origin to an arbitrary point) with the constraint that the arbitrary point must lie on the plane. Hint: minimizing the square of the distance also minimizes the distance.
     
    Last edited: Oct 28, 2011
  6. Oct 28, 2011 #5

    gneill

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    Staff: Mentor

    You should be able to write a normal to the plane by inspection of the defining equation. Any line that is perpendicular to the plane must be parallel to this normal. So write a parametric equation of a line that passes through the origin that lies along this normal vector. Where does this line intersect the plane?
     
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