Which of the following is not equal to w cdot | vedclass

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(D) The scalar triple product of three vectors $a, b, c$ is defined as $a \cdot(b 	imes c)$.It follows the cyclic property: $a \cdot(b 	imes c) = b

Vedclass · Accepted Answer

$v \cdot(u 	imes w)$

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(D) The scalar triple product of three vectors $a, b, c$ is defined as $a \cdot(b 	imes c)$.It follows the cyclic property: $a \cdot(b 	imes c) = b \cdot(c 	imes a) = c \cdot(a 	imes b)$.Given the expression $w \cdot(u 	imes v)$,by the cyclic property,this is equal to $u \cdot(v 	imes w)$ and $v \cdot(w 	imes u)$.Also,since the dot product is commutative,$w \cdot(u 	imes v) = (u 	imes v) \cdot w$.However,$v \cdot(u 	imes w) = -(v \cdot(w 	imes u)) = -(w \cdot(u 	imes v))$.Therefore,$v \cdot(u 	imes w)$ is not equal to $w \cdot(u 	imes v)$.

Which of the following is not equal to $w \cdot(u \times v)$ ?

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