identify the point on the line of intersection of the two planes that is nearest to the point (2,1,1) not on this line
p1: x + 2y - z - 1 = 0
p2: x + y + z - 3 = 0
The Attempt at a Solution
I think I can find the line of intersection by crossing the two normal vectors from p1 and p2
so N3 = <1,2,-1> x <1,1,1> and then trying to minimize the distance from the point (2,1,1) to N3 by differentiating the distance formula using the x,y,z parameters.