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)`

Options

A. 1
B. 2
C. 3
D. 4

Answer

D

Explanation

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)`