Or search by topic
Let P_1 be a plane through the points A(2,1,0), B(1,1,1) and C(1,7,3) and P_2 be a plane through the points A, B and V(x,y,z).
Find all the points V(x,y,z) such that the two planes are perpendicular.
See how 4 dimensional quaternions involve vectors in 3-space and how the quaternion function F(v) = nvn gives a simple algebraic method of working with reflections in planes in 3-space.