Write the distributive law for the product of two vectors.

The distributive law for the scalar product (dot product) of a vector $\vec{A}$ with the sum of two vectors $\vec{B}$ and $\vec{C}$ is given by:
$\vec{A} \cdot (\vec{B} + \vec{C}) = \vec{A} \cdot \vec{B} + \vec{A} \cdot \vec{C}$
Similarly,for the vector product (cross product):
$\vec{A} \times (\vec{B} + \vec{C}) = \vec{A} \times \vec{B} + \vec{A} \times \vec{C}$
This law states that the product of a vector with the sum of two other vectors is equal to the sum of the individual products of the vector with each of the other two vectors.