Statement-$1$: Vectors $\vec{a}, \vec{b},$ and $\vec{c}$ are coplanar if and only if $\vec{a} \cdot (\vec{b} \times \vec{c}) = 0$.
Statement-$2$: Vectors $\vec{u}$ and $\vec{v}$ are perpendicular if and only if $\vec{u} \cdot \vec{v} = 0$,where $\vec{u} \times \vec{v}$ is a vector perpendicular to the plane of $\vec{u}$ and $\vec{v}$.

• A
  Statement-$1$ is true,Statement-$2$ is true. Statement-$2$ is the correct explanation for Statement-$1$.
• B
  Statement-$1$ is true,Statement-$2$ is true. Statement-$2$ is not the correct explanation for Statement-$1$.
• C
  Statement-$1$ is true,Statement-$2$ is false.
• D
  Statement-$1$ is false,Statement-$2$ is true.