The volume of the parallelopiped whose edges are OA-2-3-0k- OB-k- and OC-3-3k- is-

The correct option is D none of the aboveVolume is [OA,OB,OC] =[ 2 amp; 3 amp; 0 1 amp; 1 amp; 1 nbsp; 3 amp; 0 amp; 3 ] ...

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Applications Scalar Triple Product

The volume of...

Question

The volume of the parallelopiped whose edges are $- - \to O A = 2^i - 3^j + 0^k,$ $- - \to O B =^i +^j -^k$ and $- - \to O C = 3^i - 3^k$ is:

\frac{4}{13}

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4

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\frac{2}{7}

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none of the above

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Solution

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

3^i -^k

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

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

4

- - \to O A = 2^i + 3^j -^k, - - \to O B =^i - 2^j + 3^k, - - \to O C = 3^i + 4^j - 2^k and - - \to O D =^i - 6^j + 6^k

O

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

\to u =^i +^j + λ^k, \to v =^i +^j + 3^k

\to w = 2^i +^j +^k

1

θ

\to u

\to w

cos θ

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