Let and be unit vectors

MATHEMATICS · Subjective · A Level · Mathematics · Vectors · Vectors

Problem

Let

\hat{\mathbf{u}}

and

\hat{\mathbf{v}}

be unit vectors. If

\mathbf{w}

is a vector such that

\mathbf{w} + (\mathbf{w} \times \mathbf{u}) = \mathbf{v}

, then prove that

|(\mathbf{u} \times \mathbf{v}) \cdot \mathbf{w}| \le \frac{1}{2}

and that the equality holds if and only if

\mathbf{u}

is perpendicular to

\mathbf{v}