Question

If the volume of the parallelopiped formed by the vectors `veca, vecb, vecc` as three coterminous edges is 27 units, then the volume of the parallelopiped having `vec(alpha)=veca+2vecb-vecc, vec(beta)=veca-vecb`
and `vec(gamma)=veca-vecb-vecc` as three coterminous edges, is
A. 27 cubic units
B. 9 cubic units
C. 81 cubic units
D. none of these

Answer 1

Correct Answer - C
We have `|[(veca, vecb, vecc)]|=27` cubic units
Now, `[(vec(alpha),vec(beta), vec(gamma))]=|(1, 2, -1),(1,-1, 0),(1,-1,-1)|[(veca, vecb, vecc)]`
`implies[(vec(alpha),vec(beta),vec(gamma))]=3[(veca, vecb, vecc)]`
`:.` Required volume `=|[vec(alpha),vec(beta),vec(gamma)]|`
`=3|[(veca, vecb, vecc)]|=3xx27=81` cubic units