If and are the three unit vectors and and are scalars such that

MATHEMATICS · Subjective · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

\hat{a}, \hat{b}

and

\hat{c}

are the three unit vectors and

\alpha, \beta

and

\gamma

are scalars such that

\hat{c} = \alpha\hat{a} + \beta\hat{b} + \gamma(\hat{a} \times \hat{b})

. If it is given that

\hat{a} \cdot \hat{b} = 0

and

\hat{c}

makes equal angle with both

\hat{a}

and

\hat{b}

, then evaluate

\alpha^2 + \beta^2 + \gamma^2