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Unit Vectors

The volume of...

Question

The volume of parallelopiped with vectors $\to a + 2 \to b - \to c, \to a - \to b, \to a - \to b - \to c$ as coterminous edges is $k [\to a \to b \to c],$ then $k$ is

A

- 2

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B

2

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C

3

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D

- 3

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Solution

The correct option is C $3$
$k [\to a \to b \to c] = ∣ ∣ ∣ ∣ \begin{matrix} 1 & 2 & - 1 1 & - 1 & 0 1 & - 1 & - 1 \end{matrix} ∣ ∣ ∣ ∣ [\to a \to b \to c]$
$\Rightarrow k = 1 (1 - 0) - 2 (- 1 - 0) - 1 (- 1 + 1) = 3$

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