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Calculus and Vectors

if u and v are non-collinear vectors, show that u, uxv, and (uxv)xu are mutually orthogonal

By definition the cross product of vectors $\vec a$ and $\vec b$ is orthogonal to the plane containing $\vec a$ and $\vec b$ . So $\vec u$ being orthogonal to $\vec u x \vec v$ is by definition. And $(\vec u x \vec v) x \vec u$ must be orthogonal to both $\vec u x \vec v$ and $\vec u$ .

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