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Statement 1: Let V(1) be the volume of a...

Statement 1: Let `V_(1)` be the volume of a parallelopiped ABCDEF having `veca, vecb, vecc` as three coterminous edges and `V_(2)` be the volume of the parallelopiped `PQRSTU` having three coterminous edges as vectors whose magnitudes are equal to the areas of three adjacent faces of the parallelopiped `ABCDEF`. Then `V_(2)=2V_(1)^(2)`
Statement 2: For any three vectors `vec(alpha), vec(beta), vec(gamma)`
`[vec(alpha)xxvec(beta),vec(beta)xxvec(gamma),vec(gamma)xxvec(alpha)]=[(vec(alpha),vec(beta),vec(gamma))]^(2)`

A

1. statement -1 is true, statement -2 is a correct explanation for statement -1

B

2. statement-1 is true, statement-2 is not correct explanation for statement - 1

C

3. statement -1 is true , statement-2 is false

D

4. statement-1 is false, statement-2 is correct

Text Solution

Verified by Experts

The correct Answer is:
D
Clearly statement2 is true.
Thre cotermious edges of parallelopiped `PQRSTU` are `vecaxxvecb, vecbxxvecc` and `veccxxveca`
`:.V_(2)=|[(vecaxxvecb,vecbxxvecc,vecxxveca)]|`
`impliesV_(2)=|[(veca, vecb, vecc)]^(2)|` [Using statement-2]
`impliesV_(2)=|[(veca, vecb, vecc)]|^(2)impliesV_(2)=V_(1)^(2)`
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