If three vectors $\vec{a}$, $\vec{b}$ and $\vec{c}$ are coplanar, then their scalar triple product $\vec{a} \cdot (\vec{b} \times \vec{c})$ equals:

The scalar triple product $\vec{a} \cdot (\vec{b} \times \vec{c})$ equals the **signed volume** of the parallelepiped with $\vec{a}, \vec{b}, \vec{c}$ as edges (so option D is partly correct in general, but not specifically when the vectors are coplanar). If the three vectors are coplanar, the parallelepiped degenerates to a flat figure with zero volume. Hence the scalar triple product is zero. Equivalently, $\vec{b} \times \vec{c}$ is perpendicular to the plane containing $\vec{b}$ and $\vec{c}$. If $\vec{a}$ also lies in that plane, it is perpendicular to $\vec{b} \times \vec{c}$, so the dot product is zero.