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