Question

Knowing the fact that the cross product of two vectors uxv is orthogonal to both vectors u and v, find a case where this is not applicable.

Answer 1

If two nonzero vectors $\vec u$ and $\vec v$ are collinear, then their cross product is zero vector.

The zero vector is perpendicular to all vectors.

If at least one of two vectors $\vec u$ and $\vec v$ is zero vector, then their cross product is zero vector.

The zero vector is perpendicular to all vectors.