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

Answer

A

Explanation

Since, a, b, and c are coplanar.
`implies |(alpha,2,beta),(1,1,0),(0,1,1)|=0`
`implies alpha (1-0)-2(1-0)+beta (1-0)=0`
`implies alpha +beta =2` which is possible for `alpha=1, beta =1`.