a, b, c are three non-zero,non-coplanar vecto | vedclass

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(B) Let $V = a \cdot (b 	imes c) = [a, b, c]$.Given $p = \frac{b 	imes c}{V}$,$q = \frac{c 	imes a}{V}$,$r = \frac{a 	imes b}{V}$.Then $[p, q, r]

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$\frac{1}{a \cdot (b 	imes c)}$

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(B) Let $V = a \cdot (b 	imes c) = [a, b, c]$.Given $p = \frac{b 	imes c}{V}$,$q = \frac{c 	imes a}{V}$,$r = \frac{a 	imes b}{V}$.Then $[p, q, r] = p \cdot (q 	imes r) = \frac{b 	imes c}{V} \cdot \left( \frac{c 	imes a}{V} 	imes \frac{a 	imes b}{V} ight)$.Using the vector identity $(c 	imes a) 	imes (a 	imes b) = [c, a, b] a - [c, a, a] b = [a, b, c] a - 0 = V a$.Thus,$[p, q, r] = \frac{1}{V^3} (b 	imes c) \cdot (V a) = \frac{V}{V^3} (b 	imes c) \cdot a = \frac{V^2}{V^3} = \frac{1}{V} = \frac{1}{a \cdot (b 	imes c)}$.

$a, b, c$ are three non-zero,non-coplanar vectors and $p, q, r$ are three other vectors such that $p = \frac{b \times c}{a \cdot (b \times c)}$,$q = \frac{c \times a}{a \cdot (b \times c)}$,$r = \frac{a \times b}{a \cdot (b \times c)}$. Then $[p, q, r]$ equals

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