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Statement 1: Let veca, vecb, vecc be thr...

Statement 1: Let `veca, vecb, vecc` be three coterminous edges of a parallelopiped of volume `V`. Let `V_(1)` be the volume of the parallelopiped whose three coterminous edges are the diagonals of three adjacent faces of the given parallelopiped. Then `V_(1)=2V`.
Statement 2: For any three vectors, `vecp, vecq, vecr`
`[(vecp+vecq, vecq+vecr,vecr+vecp)]=2[(vecp,vecq,vecr)]`

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
A
Statement -2 is true
We have
`V=|[(veca, vecb, vecc)]|` and `V_(1)=2|[(veca+vecb, vecb+vecc, vecc+veca)]|`
Using statement 2 we have
`V_(1)=2[(veca, vecb, vecc)]|=2V_(1)`
So statement -1 is true and statement 2 is a correct explanation for statement -1.
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