I hope the diagram is clear. If you remember locus from complex numbers, it means the region that this point could be in. Since the requirement was to be equidistant to the planes, you find the planes that act as angle bisectors to p1 and p2 that pass through "l" since the intersection line l is also equidistant to p1 and p2. To find the diagonal vector, i added the 2 normal vectors, making sure they were equal lengths. And that's it.