Let `veca, vecb, vecc` be three non-zero non coplanar vectors and `vecp, vecq` and `vecr` be three vectors given by `vecp=veca+vecb-2vecc, vecq=3veca-2vecb+vecc` and `vecr=veca-4vcb+2vecc` If the volume of the parallelopiped determined by `veca, vecb` and `vecc` is `V_(1)` and that of the parallelopiped determined by `veca, vecq` and `vecr` is `V_(2)`, then `V_(2):V_(1)=`A. `3:1`B. `7:1`C. `11:1`D. `15:1`

Let `veca, vecb, vecc` be three non-zero non coplanar vectors and `vec

1.	Let `veca, vecb, vecc` be three non-zero non coplanar vectors and `vecp, vecq` and `vecr` be three vectors given by `vecp=veca+vecb-2vecc, vecq=3veca-2vecb+vecc` and `vecr=veca-4vcb+2vecc` If the volume of the parallelopiped determined by `veca, vecb` and `vecc` is `V_(1)` and that of the parallelopiped determined by `veca, vecq` and `vecr` is `V_(2)`, then `V_(2):V_(1)=`A. `3:1`B. `7:1`C. `11:1`D. `15:1`
Answer» Correct Answer - D We have `V_(1)=[(veca, vecb, vecc)]` and `V_(2)=[(vecp, vecq, vecr)]` Now, `V_(2)=[(vecp, vecp, vecr)]` `impliesV_(2)=\|(1,1,-2),(3,-2,1),(1,-4,2)\|[(veca, vecb, vecc)]` `impliesV_(2)=15V_(1)impliesV_(2):V_(1)=15:1`

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