For three vectors u, v, w,which of the follow | vedclass

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(C) The scalar triple product is defined as $[u, v, w] = u \cdot (v 	imes w)$.By the properties of the scalar triple product,cyclic permutations of t

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$v \cdot (u 	imes w)$

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(C) The scalar triple product is defined as $[u, v, w] = u \cdot (v 	imes w)$.By the properties of the scalar triple product,cyclic permutations of the vectors do not change the value of the product.Thus,$u \cdot (v 	imes w) = v \cdot (w 	imes u) = w \cdot (u 	imes v) = [u, v, w]$.Checking the options:Option $A$: $u \cdot (v 	imes w) = [u, v, w]$.Option $B$: $(v 	imes w) \cdot u = u \cdot (v 	imes w) = [u, v, w]$.Option $C$: $v \cdot (u 	imes w) = -[u, v, w]$ (since swapping two vectors changes the sign).Option $D$: $(u 	imes v) \cdot w = [u, v, w]$.Therefore,option $C$ is not equal to the other three.

For three vectors $u, v, w$,which of the following expressions is not equal to the other three?

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