Statement 1: The vectors $\vec{a}, \vec{b}$ and $\vec{c}$ lie in the same plane if and only if $\vec{a}…
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 $\vec{v}$
Statement 1 is false, Statement 2 is true.
Statement 1 is true, Statement 2 is true, Statement 2 is correct explanation for Statement 1.
Statement 1 is true, Statement 2 is false.
Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.
Solution
Statement - 1
The vectors $\vec{a}, \vec{b}$ and $\vec{c}$ lie in the same plane.
$\Rightarrow \vec{a}, \vec{b}$ and $\vec{c}$ are coplanar.
We know, the necessary and sufficient conditions for three vectors to be coplanar is that $[\vec{a} \vec{b} \vec{c}]=0$
i.e. $\vec{a} \cdot(\vec{b} \times \vec{c})=0$
Hence, statement-1 is true.