The vector `veca=alpha hati+2hatj+betahatk` lies in the plane of vectors `vecb=hati+hatj and vecc=hatj+hatk` and bisects the angle between `vecb and vecc`. Then which one of the following gives possible values o `alpha and beta? (A) `alpha=2, beta=1` (B) `alpha=1, beta=1` (C) `alpha=2, beta=1` (D) `alpha=1, beta=2`

Options

A. `alpha=2, beta=2`
B. `alpha=1, beta=2`
C. `alpha=2,beta=1`
D. `alpha=1 , beta=1`

Answer

D

Explanation

`because veca` lies in the plane of `vecb` and `vecc`
`therefore veca=vecb+lambda vecc`
`rArr alphahati+2hatj+betahatk=hati+hatj+lambda(hatj+hatk)`
`rArr alpha=1,2 = 1+lambda , beta=lambda rArr alpha =1, beta=1`