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how do you find the coordinates of the point (x, y, z) on the plane z = 1 x + 1 y + 2 which is closest to the origin

  • math -

    the closest point is surely on a line from (0,0,0) meeting the plane at right angles.
    but the normal to the given plane is (1,1,-1)
    so the line must have direction (1,1,-1)
    it's parametric equations would be:
    x = k
    y = k
    z = -k

    sub that in to the plane to find the value of k, sub back in the parametrics
    and voila, there is your point.

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