Let b be a vector and n a unit vector. (a) Use the Levi-Civit`a symbol to prove that b = (b n) n

Let b be a vector and ^ˆn a unit vector.

(a) Use the Levi-Civit`a symbol to prove that b = (b · ˆn) ˆn + ˆn × (b × ˆn).

(b) Interpret the decomposition in part (a) geometrically.

(c) Let ω = a · (b × c) where a, b, and c are any three non-coplanar vectors. Now let

Express Ω = A · (B × C) entirely in terms of ω.

A = bxc B = 3 . axb