The volume of the parallelepiped whose sides are given by O-A- - 2- - 2- O-B- - - - - - k- and O-C- - 3- - k- is

The correct option is D 2 Volume of parallelepiped #160; = [a⃗ b⃗ c⃗] V= #160;2 amp; 2 amp; 0 1 amp; 1 amp; 1 3 ...

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The volume of...

Question

The volume of the parallelepiped whose sides are given by $\to O A = 2^i - 2^j$ , $\to O B =^i +^j -^k$ and $\to O C = 3^i -^k$ is

\frac{4}{13}

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4

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\frac{2}{7}

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2

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\to A B = 3^i - 2^j +^k

\to B C =^i + 2^j -^k

\to C D = 2^i +^j + 3^k

\to O A =^i +^j +^k

\to O D

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

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

⎡ ⎢ ⎢ ⎣ \begin{matrix} \to O A \times \to O B =^i -^j +^k \to O B \times \to O C =^i \to O C \times \to O A = -^i +^j \end{matrix} ⎤ ⎥ ⎥ ⎦

∣ ∣ \to C A \times \to C B ∣ ∣

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

\to A B = 2^i -^j +^k

\to O B = 3^i - 4^j + 4^k

\to O A

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