8. Let us rotate a vector $p$ by an angle $\theta$ about an axis $w$. (a) Represent $p$ as a projection onto $w$ and its complement. (b) Rotate the complement vector about $w$ by $\theta$. (c) Show that the rotated vector $q$ is represented as follows: $$ q=\left(I+\sin \theta[w]+(1-\cos \theta) [w]^{2} ight) p. $$ sp.vs.036