Statement $1$: The vectors $\vec{a}, \vec{b}$ and $\vec{c}$ lie in the same plane if and only if $\vec{a} \cdot (\vec{b} \times \vec{c}) = 0$.
Statement $2$: The 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 false,Statement $2$ is true.
• B
  Statement $1$ is true,Statement $2$ is true,Statement $2$ is the correct explanation for Statement $1$.
• C
  Statement $1$ is true,Statement $2$ is false.
• D
  Statement $1$ is true,Statement $2$ is true,Statement $2$ is not the correct explanation for Statement $1$.