Question

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.
• C. 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 1.

Answer 1

Answer: (C)

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 $\left[\vec{a}\vec{b}\vec{c}\right]=0$
$i.e.\vec{a}\cdot \left(\vec{b}\times \vec{c}\right)=0$
Hence, statement-1 is true.