For three vectors a, b, c,the value of [a tim | vedclass

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(B) We know that the scalar triple product is defined as $[x, y, z] = (x 	imes y) \cdot z$.Here,$[a 	imes b, b 	imes c, c 	imes a] = ((a 	imes b)

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$[a, b, c]^2$

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(B) We know that the scalar triple product is defined as $[x, y, z] = (x 	imes y) \cdot z$.Here,$[a 	imes b, b 	imes c, c 	imes a] = ((a 	imes b) 	imes (b 	imes c)) \cdot (c 	imes a)$.Using the property of vector triple products,$(a 	imes b) 	imes (b 	imes c) = [a, b, c]b$.Substituting this into the expression,we get:$[a 	imes b, b 	imes c, c 	imes a] = ([a, b, c]b) \cdot (c 	imes a)$.$= [a, b, c] (b \cdot (c 	imes a))$.$= [a, b, c] [b, c, a]$.Since the scalar triple product is cyclic,$[b, c, a] = [a, b, c]$.Therefore,the value is $[a, b, c] \cdot [a, b, c] = [a, b, c]^2$.

For three vectors $a, b, c$,the value of $[a \times b, b \times c, c \times a]$ is equal to:

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