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If veca, vecb, vecc are unit vectors suc...

If `veca, vecb, vecc` are unit vectors such that `veca. vecb=0, (veca-vecc).(vecb+vecc)=0` and `vecc=lambdaveca+muvecb+omega(veca xx vecb)`, where `lambda, mu, omega` are scalars, then

A

`mu^(2)+omega^(2)=1`

B

`lambda+mu=1`

C

`(mu+1)^(2)+mu^(2)+omega^(2)=1`

D

`lambda^(2)+mu^(2)=1`

Text Solution

Verified by Experts

The correct Answer is:
C
`(veca-vecc).(vecb+vecc)=0`
`rArr veca.vecb+vecc(veca-vecb)-|vecc|^(2)=0`
`rArr (veca-vecb).vecc=1`
`rArr (veca-vecb).(lambdaveca+muvecb+omega(veca xx vecb))=`
`rArr lambda-mu=1`
`rArr lambda=mu+1`
Now, `veca.vecb=0 rArr veca,vecb, veca xx vecb` are mutually perpendicular.
`|vecc|=1 rArr lambda^(2)+mu^(2)+omega^(2)=1`
`rArr (mu+1)^(2)+mu^(2)+omega^(2)=1`
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