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A unit vector veca in the plane of vecb=...

A unit vector `veca` in the plane of `vecb=2hati+hatj` and `vecc=hati-hatj+hatk` is such that angle between `veca` and `vecd` where `vecd=vecj+2veck` is

A

`(veci+vecj+veck)/sqrt(3)`

B

`(veci-vecj+veck)/sqrt(3)`

C

`(2veci+vecj)/sqrt(5)`

D

`(2veci-vecj)/sqrt(5)`

Text Solution

Verified by Experts

The correct Answer is:
B
Let `veca=lambdavecb+muvecc`, then `(veca.vecb)/(ab) = (veca.vecd)/(ad)`
`rArr ((lambdavecb.vecb+muvecc.vecb))/(b) = (lambdavecb.vecd+muvecc.vecd)/(d)`
`rArr (5lambda+mu)/sqrt(5) = (lambda+mu)/sqrt(5)`
`rArr lambda=0`
`therefore a=(hati-hatj+hatk)/sqrt(3)`
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