Write the necessary condition for the scalar product of two mutually perpendicular vectors.

(N/A) The scalar product (dot product) of two vectors $\vec{A}$ and $\vec{B}$ is defined as $\vec{A} \cdot \vec{B} = |A||B| \cos \theta$,where $\theta$ is the angle between the two vectors.
For two vectors to be mutually perpendicular,the angle between them must be $\theta = 90^{\circ}$.
Substituting this into the formula,we get $\vec{A} \cdot \vec{B} = |A||B| \cos(90^{\circ})$.
Since $\cos(90^{\circ}) = 0$,the scalar product becomes $\vec{A} \cdot \vec{B} = 0$.
Therefore,the necessary condition for two non-zero vectors to be mutually perpendicular is that their scalar product must be zero.