Vector equations of plane

There are 2 NRICH Mathematical resources connected to Vector equations of plane
Walls
problem

Walls

Age
16 to 18
Challenge level
filled star filled star filled star
Plane 1 contains points A, B and C and plane 2 contains points A and B. Find all the points on plane 2 such that the two planes are perpendicular.
Quaternions and Reflections
problem

Quaternions and reflections

Age
16 to 18
Challenge level
filled star filled star filled star
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.