Vectors - 3D Math Primer for Graphics and Game Development - page 77

23. In the derivation of a matrix to scale along an arbitrary axis, we reach a
step where we have the vector expression

′

p = p + (k −1) (pn) n,

where n is an arbitrary vector [n x , n y , n z ] and k is an arbitrary scalar, but
p is one of the cardinal axes. Plug in the value p = [1, 0, 0] and simplify
the resulting expression for p ′ . The answer is not a vector expression, but
a single vector, where the scalar expressions for each coordinate have been
simplified.
24. A similar problem arises with the derivation of a matrix to rotate about
an arbitrary axis. Given an arbitrary scalar θ and a vector n, substitute
p = [1, 0, 0] and simplify the value of p ′ in the expression

p ′ = cos θ (p−(pn) n) + sin θ (n×p) + (pn) n.

What's our vector, Victor?
— Captain Oveur in Airplane! (1980)