(827, #27) Find the shortest distance from the point (2, -2, 3) to the plane

6x + 4 y - 3 z = 2.

Solution: Let (x,y,z) be any point on the plane. The problem is one of minimizing

subject to the constraint 6x + 4 y - 3 z = 2.

Lagrange's equations give

Using the constraint:

Thus the minimal distance is

by:rjm