I came across a problem which requires to prove that plane ax+by+cz=0 cuts cone xy+yz+xz=0 in perpendicular lines if 1/a+1/b+1/c=0 Solution to the problem says that since given cone is generated by three mutually perpendicular planes, hence plane ax+by+cz=0 will cut it in perpendicular lines if normal to plane through vertex (0,0,0) lies on cone itself.
I am unable to visualise graphically how such a plane can cut cone in perpendicular lines. Why is it necessary for normal to plane through (0,0,0) to lie on cone?
I am assuming that lines being referred in question are the boundaries of the cone which plane would touch when cutting across cone. Any graph/picture would be thankful.