If $\mathbf{x} \cdot \mathbf{a} = 0, \mathbf{x} \cdot \mathbf{b} = 1, [\mathbf{x} \mathbf{a} \mathbf{b}] = 1$ …

Mathematics

Problem

\mathbf{x} \cdot \mathbf{a} = 0, \mathbf{x} \cdot \mathbf{b} = 1, [\mathbf{x} \mathbf{a} \mathbf{b}] = 1

and

\mathbf{a} \cdot \mathbf{b} \ne 0

, then find

\mathbf{x}

in terms of

\mathbf{a}

and

\mathbf{b}