Mathematics

Problem

Let

\hat{u}

and

\hat{v}

are unit vectors and

\mathbf{w}

is a vector such that

\hat{u} \times \hat{v} + \hat{u} = \mathbf{w}

and

\mathbf{w} \times \hat{u} = \hat{v}

, then find the value of

[\hat{u} \hat{v} \mathbf{w}]