The vector lies in the plane of the vectors and and bisects the angle between and

MATHEMATICS · Single correct · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

The vector

\mathbf{a} = \alpha\hat{i} + 2\hat{j} + \beta\hat{k}

lies in the plane of the vectors

\mathbf{b} = \hat{i} + \hat{j}

and

\mathbf{c} = \hat{j} + \hat{k}

and bisects the angle between

\mathbf{b}

and

\mathbf{c}

. Then, which one of the following gives possible values of

\alpha

and

\beta

? (1)

\alpha = 1, \beta = 1

(2)

\alpha = 2, \beta = 2

(3)

\alpha = 1, \beta = 2

(4)

\alpha = 2, \beta = 1