Question

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

Answer 1

I f 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.