3d Geometry

We are given two planes: Plane 1: Plane 2: Let the equation of a plane through their intersection be: Expand: Group like terms: This is the general form of the plane through the line of intersection. We now require this plane to be parallel to the x-axis. So the direction vector must lie on the plane. That means the normal vector of the plane should be orthogonal to From (1), the normal vector is: For the plane to be parallel to the x-axis, we must have: Substitute into (1): - Coefficient of : - Coefficient of : - Coefficient of : - Constant term: So the equation becomes: Final Answer: