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If vec a , vec ba n d vec c are three n...

If ` vec a , vec ba n d vec c` are three non coplanar vectors, then `( veca + vecb + vecc )[( veca + vecb )×( veca + vecc )]` is :

A

0

B

`[veca vecb vecc]`

C

`2[veca vecb vecc]`

D

`-[veca vecb vecc]`

Text Solution

Verified by Experts

The correct Answer is:
d
`(veca+ vecb+vecc).[(veca+vecb)xx(veca+vecc)]`
`= (veca+vecb+vecc).[veca xx veca +vecaxx vecc+vecb xx veca +vecbxxvecc]`
`= (veca +vecb +vecc).[veca xx vecc +vecb xx veca+vecb xxvecc]`
`[veca vecb vecc] -[veca vecb vecc]-[veca vecb vecc]`
`-[veca vecb vecc]`
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