Question

Find the coordinates of the point (x,y,z)(x,y,z) on the plane z=2x+3y+3z=2x+3y+3 which is closest to the origin.

Answer 1

The vector equation of the line through the origin perpendicular to the plane is
.. (x, y, z) = t(2, 3, -1)
so the point of interest will satisfy
.. 2(2t) +3(3t) -(-t) = -3
.. 14t = -3
.. t = -3/14
and its coordinates are (x, y, z) = (-3/7, -9/14, 3/14)