Question

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

Answer: (C)

Statement-1: $\overrightarrow{PQ}\times (\overrightarrow{RS}\times \overrightarrow{ST})\ne 0.$
Since $\overrightarrow{PQ}$ is not parallel to $\overrightarrow{RT}$, we get
$\overrightarrow{PQ}\times (\overrightarrow{RT})$
That is, Statement-2 is true.

$\overrightarrow{PQ}\times (\overrightarrow{RT})\ne 0$
Statement-2: $\overrightarrow{PQ}\times \overrightarrow{RS}=\overrightarrow{0}$ and $\overrightarrow{PQ}\times \overrightarrow{ST}\ne \overrightarrow{0}$
Since $\overrightarrow{PQ}$ is not parallel to $\overrightarrow{RS}$, Statement-2 is false.