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## Homework Statement

Determine the scalar equation of the plane that contains the line of the intersection of the planes x+y+z=4 and y+z=2, if the plane is two units from the origin.

## Homework Equations

direction of intersecting line is M = N

_{1}× N

_{1}

## The Attempt at a Solution

Let y= 0, find a POI of two planes

x=2, z=2

Therefore one POI is (2,0,2)

Direction of Line is M = N

_{1}× N

_{1}= [1,1,1] × [0,1,1]

Would there not be multiple solutions to this problem because there are multiple of planes that can be rotated around the line of intersection that are all two units from the origin?