Given two planes with equations x + 2y + z = 1 and x - 2y + 3z = 3,
(a) Show that the planes are orthogonal.
(b) Find the plane that is orthogonal to the given ones and passes through the point
a vector normal to the first plane is (1, 2, 1) and a vector normal to the second is (1, -2, 3);
the dot product of these two normals is 1 - 4 + 3 = 0; hence, the planes ...
This provides an example of working with orthogonal planes.