The vector a = α i + 2 j + β k lies in the plane of the vectors b = i + j and c = j + k and bisects the angle between b and c.Then which one of the following gives possible values of α and β ?

Vector Algebra: JEE Main 2008 Mathematics question

JEE Main 2008 · Annual, Paper 1 · Q5712

JEE Main 2008Annual, Paper 1MathematicsMediumVector Algebra184× since 2002

The vector

\overrightarrow a = \alpha \widehat i + 2\widehat j + \beta \widehat k

lies in the plane of the vectors

\overrightarrow b = \widehat i + \widehat j

and

\overrightarrow c = \widehat j + \widehat k

and bisects the angle between

\overrightarrow b

and

\overrightarrow c

.Then which one of the following gives possible values of

\alpha

and

\beta