Question

Assertion :Let the vectors $\overline{PQ},\overline{QR},\overline{RS},\overline{ST},\overline{TU}$ and $\overline{UP}$ represent the sides of a regular hexagon.
STATEMENT-$1$: $\overline{PQ}\times (\overline{RS}+\overline{ST})\ne \overrightarrow{0}$. Reason: STATEMENT-$2$: $\overline{PQ}\times \overline{RS}=\overrightarrow{0}$ and $\overrightarrow{PQ}\times \overrightarrow{ST}\ne \overrightarrow{0}$.

• A. Statement -$1$ is True, Statement -$2$ is True; Statement-$2$ is a correct explanation for Statement-$1$
• B. Statement -$1$ is True, Statement -$2$ is True; Statement-$2$ is NOT a correct explanation for Statement-$1$
• C. Statement -$1$ is True, Statement -$2$ is False
• D. Statement -$1$ is False, Statement -$2$ is True

Answer 1

The correct option is C Statement -$1$ is True, Statement -$2$ is False

Since $\overline{PQ}||\overline{TR}$ .$\cdot \overline{TR}$ is resultant of $\overline{SR}$ and $\overline{ST}$ vector.
$\Rightarrow \overline{PQ}\times (\overline{RS}+\overline{ST})\ne 0$

But for statement $2$, we have $\overline{PQ}\times \overline{RS}=\overrightarrow{0}$
which is not possible as $\overline{PQ}||\overline{RS}$
Hence, statement $1$ is true and statement $2$ is false.