If a cdot b = b cdot c = c cdot a = 0,then wh | vedclass

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(C) Given that $a \cdot b = 0$,$b \cdot c = 0$,and $c \cdot a = 0$. This implies that the vectors $a$,$b$,and $c$ are mutually orthogonal to each othe

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$|a||b||c|$

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(C) Given that $a \cdot b = 0$,$b \cdot c = 0$,and $c \cdot a = 0$. This implies that the vectors $a$,$b$,and $c$ are mutually orthogonal to each other. Let $a$,$b$,and $c$ be represented as vectors along the coordinate axes $X$,$Y$,and $Z$ respectively,such that $a = |a|i$,$b = |b|j$,and $c = |c|k$. The scalar triple product is defined as $[a b c] = (a 	imes b) \cdot c$. Substituting the values,we get $a 	imes b = (|a|i 	imes |b|j) = |a||b|k$. Then,$[a b c] = (|a||b|k) \cdot (|c|k) = |a||b||c|(k \cdot k) = |a||b||c|(1) = |a||b||c|$. Thus,the value of the scalar triple product is $|a||b||c|$.

If $a \cdot b = b \cdot c = c \cdot a = 0$,then what is the value of the scalar triple product $[a b c]$?

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