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Statement $1$ : The vectors $\vec a ,\vec b$ and $\vec c$ lie in the same plane if and only if $\vec a.\left( {\vec b \times \vec c} \right) = 0$
Statement $2$ : The vectors $\vec u$ and $\vec v$ are perpendicular if and only if $\vec u.\vec v = 0$ 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 correct explanation for Statement $1$ .
• ✓
  Statement $1$ is true, Statement $2$ is false.
• D
  Statement $1$ is true, Statement $2$ is true, ,Statement $2$ is not a correct explanation for Statement $2$