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If veca and vecb are non-zero, non paral...

If `veca` and `vecb` are non-zero, non parallel vectors, then the value of
`|veca + vecb+veca xx vecb|^(2) +|veca + vecb-veca xx vecb|^(2)` equals

A

`(1+veca.veca)(1+vecb.vecc)`

B

`2(1+veca.veca)(1+vecb.vecb)`

C

`2{(1+veca.veca)(1+vecb.vecb)-(1-veca.vecb)^(2)}`

D

`2{(1-veca.veca)(1-vecb.vecb)+(1-veca.vecb)^(2)}`

Text Solution

Verified by Experts

The correct Answer is:
C
`|veca + vecb+veca xx vecb|^(2) + |veca+vecb-veca xx vecb|^(2)`
`=2(|veca|^(2)+|vecb|^(2)+|veca xx vecb|^(2)+2veca.vecb)`
`={1+|veca|^(2)+|vecb|^(2)+|veca|^(2)|vecb|^(2)-(veca.vecb)^(2) + 2veca.vecb-1}`
`rArr 2{(1+|veca|^(2))(1+|vecb|^(2))-(1-veca.vecb|^(2))}`
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