1. The problem statement, all variables and given/known data let p1 and p2 be planes in R3, with respective equations: x+5y-z=20 and 2x+5y+2z=20 These planes are not parallel. Find the standard equation for the plane that is orthogonal to both of these planes and contains the origin. 3. The attempt at a solution I have only managed to garner a few facts from the problem, however I don't know how to use them. Here they are: Since the plane, we'll call it ζ that we are looking for is orthogonal to both of these planes, ζ must contain the normal vectors of both of these planes. These normal vectors, for p1 and p2 respectively, are (1,5,-1) and (2,5,2). Also, the standard equation of ζ must be equal to 0, as ζ contains the origin, ie: ax+by+cz=0, since the origin is (x,y,z)=(0,0,0) That's as far as I got. The information is there, I just have no clue how to use it.