For two vectors A and B , the magnitude of their vector product can...

The magnitude of the vector product of two vectors $\vec{A}$ and $\vec{B}$ is given by $|\vec{A} \times \vec{B}| = AB \sin \theta$, where $\theta$ is the angle between the vectors.

Since the value of $\sin \theta$ lies in the range $[0, 1]$ for $\theta \in [0, \pi]$, we have $0 \le \sin \theta \le 1$.

Multiplying by $AB$, we get $0 \le AB \sin \theta \le AB$.

Thus, the magnitude of the vector product can be zero (if $\theta = 0$ or $\pi$), less than $AB$ (if $0 < \theta < \pi/2$ or $\pi/2 < \theta < \pi$), or equal to $AB$ (if $\theta = \pi/2$).

It can never be greater than $AB$.