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If V is the volume of the parallelepiped...

If V is the volume of the parallelepiped having three coterminous edges as `veca,vecb` and `vecc`, then the volume of the parallelepiped having three coterminous edges as
`vecalpha = (veca.veca)veca+(veca.vecb)vecb+(veca.vecc)vecc`,
`vecbeta=(vecb.veca)veca+(vecb.vecb)+(vecb.vecc)vecc`
and `veclambda=(vecc.veca)veca+(vecc.vecb)vecb+(vecc.vecc)vecc` is

A

3V

B

4V

C

`V^(2)`

D

`V^(3)`

Text Solution

Verified by Experts

The correct Answer is:
D
`V=[vecavecbvecc]`
`therefore [vecalphavecbetaveclambda]=|{:(veca.veca, veca.vecb, veca.vecc),(vecb.veca, vecb.vecb, vecb.vecc),(vecc.veca, vecc.vecb, vecc.vecc):}|[vecavecbvecc]`
`=[vecavecbvecc][vecavecbvecc][vecavecbvecc]=V^(3)`
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