If the volume of parallelopiped formed by the vectors a,b,c as three coterminous edges is 27 cu units, then the volume of the parallelopiped have `alpha=a+2b-c,beta=a-b and gamma=a-b-c` as three coterminous edges is

Options

A. 27 cubic units
B. 9 cubic units
C. 81 cubic units
D. none of these

Answer

C

Explanation

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