Let `vecu and vecv` be unit vectors. If `vecw` is a vector such that `vecw+vecwxxvecu=vecv`, then prove that `|(vecuxxvecv).vecw|le1/2` and that the equality holds if and only if `vecu` is perpendicular to `vecv`.

Explanation

To solve the problem, we need to prove that \( |\vec{u} \times \vec{v} \cdot \vec{w}| \leq \frac{1}{2} \) and that equality holds if and only if \( \vec{u} \) is perpendicular to \( \vec{v} \).

### Step-by-Step Solution:

1. **Start with the given equation**:
\[ \vec{w} + \vec{w} \times \vec{u} = \vec{v} \]
...