# Orthogonal planes

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

(1;-1; 2).

https://brainmass.com/math/geometry-and-topology/orthogonal-planes-218206

#### Solution Preview

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 ...

#### Solution Summary

This provides an example of working with orthogonal planes.

$2.19