Find out the volume of a prism on tringular base, the three sides of the prism meeting on a vertex are given below: $\to O A = 3 i + 4 j + 12 k, \to O B = 12 i + 3 j + 4 k,$ $\to O C = 4 i + 12 j + 3 k .$

472.5

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693.5

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945

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1387

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Solution

The correct option is B 693.5
Required volume $= \frac{1}{2} ∣ ∣ ∣ ∣ \begin{matrix} 3 & 4 & 12 12 & 3 & 4 4 & 12 & 3 \end{matrix} ∣ ∣ ∣ ∣$ $= \frac{1}{2} [3 (9 - 48) - 4 (36 - 16) + 12 (144 - 12)]$ $= \frac{1387}{2} = 693.5.$

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Similar questions

\to O A = 3 i + 4 j + 12 k, \to O B = 12 i + 3 j + 4 k,

\to O C = 4 i + 12 j + 3 k .

\to O A

\to O C .

\to O A = 3 i + 4 j + 12 k, \to O B = 12 i + 3 j + 4 k,

\to O C = 4 i + 12 j + 3 k .

\to O A = 3 i + 4 j + 12 k, \to O B = 12 i + 3 j + 4 k,

\to O C = 4 i + 12 j + 3 k .

\to O A

\to O B

13 ¯ ¯ ¯ a = 3 ¯ i + 4 ¯ j + 12 ¯ ¯ ¯ k, 13 ¯ ¯ b = 4 ¯ i - 12 ¯ j + 3 ¯ ¯ ¯ k, 13 ¯ ¯ c = 12 ¯ i + 3 ¯ j - 4 ¯ ¯ ¯ k

¯ ¯ ¯ a \times ¯ ¯ b

\to c

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