2. Demonstrate the following relationship involving the dot product and cross product (a) u. (V x W) = v. (w xu) = w. (u xv) (b) u. (u xv) = 0 (and explain geometrically why the result is zero) (c) (a × b) × (a × c) = [(a × b) · c]a (d) (a × b) · (c × d) = (a · c) (b · d) — (b · c) (a · d) (e) a × (b × c) + cx (a × b) + b × (c × a) = 0 (f) ||a+b|| ≤ ||a|| + ||b||

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