Let and be three mutually perpendicular vectors of equal magnitude

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

Problem

Let

\mathbf{a}, \mathbf{b}

and

\mathbf{c}

be three mutually perpendicular vectors of equal magnitude. If the vector

\mathbf{x}

satisfies the equation

\mathbf{a} \times \{(\mathbf{x} - \mathbf{b}) \times \mathbf{a}\} + \mathbf{b} \times \{(\mathbf{x} - \mathbf{c}) \times \mathbf{b}\} + \mathbf{c} \times \{(\mathbf{x} - \mathbf{a}) \times \mathbf{c}\} = 0

, then find

\mathbf{x}