The volume of the parallellopiped whose coterminal edges are $2^i - 3^j + 4^k,^i + 2^j - 2^k, 3^i -^j +^k$ is

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Solution

The correct option is C 7
Volume =| $∣ ∣ ∣ ∣ \begin{matrix} 2 & - 3 & 4 1 & 2 & - 2 3 & - 1 & 1 \end{matrix} ∣ ∣ ∣ ∣ | = | 2 (2 - 2) + 3 (1 + 6) + 4 (- 1 - 6) | = | 0 + 21 - 28 | = 7$ cubic units

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2^i - 3^j + 4^k,^i + 2^j - 2^k, 3^i -^j +^k

\to a = 2^i - 3^j - 4^k, \to b =^i + 2^j -^k,

\to c = 3^i +^j + 2^k

^i -^j +^k, 2^i - 4^j + 5^k,^3 i - 5^j + 2^k

\begin{matrix} \to a =^i - 2^j +^3 \to b = - 2^i + 3^j - 4^k \to c =^i - 3^j + 5^k \end{matrix}

If \to a = 2^i + 3^j +^k, \to b =^i - 2^j +^k and \to c = - 3^i +^j + 2^k,

[\to a \to b \to c] .

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