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-4vecb+2vecc`
If the volume of the parallelopiped determined by `veca, vecb` and `vecc` is `V_(1)` and that of the parallelopiped determined by `vecp, vecq` and `vecr` is `V_(2)`, then `V_(2):V_(1)=`

Options

A. `3:1`
B. `7:1`
C. `11:1`
D. `15:1`

Answer

D

Explanation

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`