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Vector Addition

The volume of...

Question

The volume of the parallelopiped whose coterminous edges are $^i -^j +^k, 2^i - 4^j + 5^k,^3 i - 5^j + 2^k$ is

A

4

cu unit

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B

3

cu unit

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C

2

cu unit

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D

8

cu unit

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Solution

The correct option is D $8$ cu unit
Let the edges are $^i -^j +^k, 2^i - 4^j + 5^k,^3 i - 5^j + 2^k$
Volume of parallelopiped,
$V = [\to a \to b \to c]$
$∴ V = ∣ ∣ ∣ ∣ \begin{matrix} 1 & - 1 & 1 2 & - 4 & 5 3 & - 5 & 2 \end{matrix} ∣ ∣ ∣ ∣$
$V = 1 (- 8 + 25) + 1 (4 - 15) + 1 (- 10 + 12)$
$= 17 - 11 + 2 = 8$ cu unit

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