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Question

If V is the volume of parallelepiped formed by the vectors a,b,c as three coterminous edges is 27 cubic units, then the volume of the parallelepiped having α=a+2bc,β=ab and γ=abc as three coterminous edges is

A
27
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B
9
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C
81
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D
48
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Solution

The correct option is A 27
Given that
[abc]=27=V (volume)

α=a+2bc
β=ab+0c
γ=abc

[αβγ]= ∣ ∣121110111∣ ∣ [abc]

=3[abc]
=27×3=81 cubic units

Hence, option C is the correct option.

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