- #1

icesalmon

- 270

- 13

## Homework Statement

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

## Homework Equations

## 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 N

_{3}= <1,2,-1> x <1,1,1> and then trying to minimize the distance from the point (2,1,1) to N

_{3}by differentiating the distance formula using the x,y,z parameters.