# Thread: vector parallel to intersection of planes

1. ## vector parallel to intersection of planes

I need to find a vector that is parallel to the intersection of the planes:
2x - 3y +5z = 2 and 4x + y - 3z = 7

After I obtain this, I need to find the equation of the plane through the origin that is perpendicular to the line of intersection of the above mentioned two planes.

My head is spinning trying to figure out where to begin! Any aid would be much appreciated. Frostking

2. I never like these questions ...

(1) Consider the cross product of the normals of the plane. The resultant vector should be parallel to the line of intersection (can you think why?).

(2) Recall that a plane can be defined by the equation: $ax + by + cz + d = 0$ where $(a,b,c)$ is a vector perpendicular to the plane. The direction vector we found for the line of intersection is perpendicular to the desired plane so why not use it as our vector $(a,b,c)$? Now, since it passes through the origin, we know that $(x,y,z) = (0, 0, 0)$ is satisfies the equation of the plane. This should be enough information.