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Scalar Triple Product

If [abc]=-4, ...

Question

If $[\to a \to b \to c] = - 4,$ then the Volume (in cubic units) of the parallelopiped with coterminous edges $\to a + 2 \to b, 2 \to b + \to c, 3 \to c + \to a$ is

64

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32

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8

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16

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Solution

The correct option is B $32$
$Volume of parallelopiped = | [\to a + 2 \to b 2 \to b + \to c 3 \to c + \to a] |$ $∣ ∣ ∣ ∣ \begin{matrix} 1 & 2 & 0 0 & 2 & 1 1 & 0 & 3 \end{matrix} ∣ ∣ ∣ ∣ | [\to a \to b \to c] | \Rightarrow 8 | [\to a \to b \to c] | \Rightarrow 8 (4) = 32$

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