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If veca, vecb and vecc are three units v...

If `veca, vecb` and `vecc` are three units vectors equally inclined to each other at an angle `alpha`. Then the angle between `veca` and plane of `vecb` and `vecc` is

A

`theta=cos^(-1)((cosalpha)/(cos(alpha/2)))`

B

`theta=sin^(-1)((cosalpha)/(cos(alpha/2)))`

C

`theta=cos^(-1)((sin(alpha/2))/(sinalpha))`

D

`theta=sin^(-1)((sin(alpha/2))/(sinalpha))`

Text Solution

Verified by Experts

The correct Answer is:
A
Let `theta` be the required angle. Then `theta` will be the angle between `veca` and `vecb + vecc'. (vecb+vecc)` lies along the angular bisector of `veca` and `vecb`.
`therefore costheta=(veca.(vecb+vecc))/(|veca||vecb+vecc|)`
`=(2cosalpha)/sqrt(2+2cosalpha) = (cosalpha)/(cos(alpha/2))`
`therefore theta=cos^(-1)((cosalpha)/(cos(alpha/2)))`
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