Anyone could help me to prove this following inequality?
$\displaystyle\frac{||(u+v)\wedge w||}{||u+v||}\le \frac{||u\wedge w||}{||u||} +\frac{||v\wedge w||}{||v||} $
where $u\wedge v$ is the wedge (cross) product of $u$ and $v$ and here we use Euclidean norm in $\mathbb{R}^n$ $||u||=\sqrt{\sum_{i=1}^n u_i^2}$,
$||u\wedge v|| = \sqrt{\sum_{1 \le i < j \le n} \left(u_iv_j-u_jv_i \right)^2 }$