Answer:
x-y-3=0
Step-by-step explanation:
Choose two common points on the line of intersection of the planes x − z = 3 and y + 2z = 3:
- 1st point: if x=0, then z=-3 and y=3-2z=3+6=9, so the 1st point is (0,-3,9);
- 2nd point: if x=3, then z=0 and y=3-2z=3-0=3, so the 2nd point is (3,0,3).
The perpendicular plane to the plane x+y-4z=6 is parallel to the vector with coordinates (1,1,-4) (normal vector of the given plane).
Hence, the equation of needed plane is
Thus,