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If a vector vecr is equall inclined with...

If a vector `vecr` is equall inclined with the vectors `veca=costhetahati+sinthetahatj, vecb=-sinthetahati+costhetahatj` and `vecc=hatk`, then the angle between `vecr` and `veca` is

A

`cos^(-1)(1/sqrt(2))`

B

`cos^(-1)(1/sqrt(3))`

C

`cos^(-1)(1/3)`

D

`cos^(-1)(1/2)`

Text Solution

Verified by Experts

The correct Answer is:
B
`veca=costhetahati+sinthetahatj`
`vecb=-sinthetahati+costhetahatj`
and `vecc=hatk`
`|veca|=|vecb|=|vecc|` and `veca.vecb=vecb.vecc=vecc.veca`
`therefore` Required angle is `cos^(-1)(1/sqrt(3))`
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