Given the following expressions: (A) (a times | vedclass

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(B) $1$. Expression $(A)$ $(a 	imes b) \cdot c$ represents the scalar triple product, which is meaningful.$2$. Expression $(B)$ $a 	imes (b \cdot c)

Vedclass · Accepted Answer

$A$ and $D$ are meaningful

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(B) $1$. Expression $(A)$ $(a 	imes b) \cdot c$ represents the scalar triple product, which is meaningful.$2$. Expression $(B)$ $a 	imes (b \cdot c)$ is meaningless because $(b \cdot c)$ is a scalar, and the cross product of a vector $a$ and a scalar is not defined.$3$. Expression $(C)$ $a \cdot (b \cdot c)$ is meaningless because $(b \cdot c)$ is a scalar, and the dot product of a vector $a$ and a scalar is not defined.$4$. Expression $(D)$ $|a|(b \cdot c)$ represents the product of a scalar $|a|$ and a scalar $(b \cdot c)$, which is meaningful.$5$. Expression $(E)$ $(a \cdot b) 	imes (b \cdot c)$ is meaningless because $(a \cdot b)$ and $(b \cdot c)$ are both scalars, and the cross product between two scalars is not defined.$6$. Thus, $(A)$ and $(D)$ are meaningful, while $(B)$, $(C)$, and $(E)$ are meaningless.

Given the following expressions: $(A)$ $(a \times b) \cdot c$, $(B)$ $a \times (b \cdot c)$, $(C)$ $a \cdot (b \cdot c)$, $(D)$ $|a|(b \cdot c)$, $(E)$ $(a \cdot b) \times (b \cdot c)$. Which of the following statements is correct regarding their mathematical meaning?

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