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Measuring Size

The volume of...

Question

The volume of the parallelopiped with its edges the vectors $^i +^j,^i + 2^j$ and $^i +^j + π^k$ is

A

\frac{π}{3}

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B

\frac{π}{4}

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C

\frac{π}{2}

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D

π

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Solution

The correct option is D $π$
volume is the absolute value of the scalar triangle product
$\to a . (\to b \times \to c) = ∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 0 1 & 2 & 0 1 & 1 & π \end{matrix} ∣ ∣ ∣ ∣$
$= 1 (2 π - 0) - 1 (π - 0) + 0$
$= 2 π - π = π$

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