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nCr Definitions and Properties

If the three ...

Question

If the three concurrent edges of a parallelepiped represent the vectors $\to a, \to b, \to c$ such that $[\begin{matrix} \to a & \to b & \to c \end{matrix}] = λ$ , then the volume of the parallelepiped whose three concurrent edges are the three concurrent diagonals of three faces of the given parallelepiped, is

A

2 λ

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B

3 λ

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C

λ

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D

None of these

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Solution

The correct option is D $2 λ$
The new edges of the new parallelepiped will be
$(\to a + \to b), (\to b + \to c), (\to c + \to a)$
Hence,
The parallelepiped thus formed will have a volume
$[(\to a + \to b) (\to b + \to c) (\to c + \to a)]$
$= 2 [\to a \to b \to c]$
$= 2 λ$
Hence,
The volume of the new parallelepiped is equal to $2 λ$ .

Hence, option $A$ .

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nCr Definitions and Properties

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