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If alpha(veca xx vecb)+beta(vecb xx vecc...

If `alpha(veca xx vecb)+beta(vecb xx vecc)+lambda(vecc xx veca)=0`, then

A

`veca,vecb,vecc` are coplanar is all `alpha,beta, lambda ne0`

B

`veca,vecb,vec` are coplanar if any one of `alpha, beta, lambda ne0`

C

`veca,vecb,vecc` are non-coplanar for any `alpha,beta,lambdane0`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A, B
we have,
`alpha(veca xx vecb) +beta(vecb xx vecc) + lambda(vecc xx veca)=0`
Taking dot product with `vecc`, we have
`alpha[vecavecbvecc]=0`
Similarly, taking dot product with b and c, we have `lamba[vecavecbvecc]=0, beta[vecavecbvecc]=0`
Now, even if one of `alpha, beta, lambda ne 0`, then we have `[vecavecbvecc]=0`
`rArr veca,vecb,vecc` are coplanar
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