Question

Assertion :Let the vectors $\overrightarrow{PQ}$,$\overrightarrow{QR}$,$\overrightarrow{RS}$,$\overrightarrow{ST}$,$\overrightarrow{TU}$ and $\overrightarrow{UP}$ represent the sides of a regular hexagon,

$\overrightarrow{PQ}\times (\overrightarrow{RS}+\overrightarrow{ST})\ne \overrightarrow{0}$

Reason: $\overrightarrow{PQ}\times \overrightarrow{RS}=\overrightarrow{0},\overrightarrow{PQ}\times \overrightarrow{ST}\ne 0$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is C Assertion is correct but Reason is incorrect

Since $\overrightarrow{PQ}$ is not parallel to $\overrightarrow{TR}$

$\because \overrightarrow{TR}$ is resultant of $\overrightarrow{RS}$ and $\overrightarrow{ST}$ vectors

$\Rightarrow \overrightarrow{PQ}\times (\overrightarrow{RS}\times \overrightarrow{ST})\ne \overrightarrow{0}$

But for reason, we have $\overrightarrow{PQ}\times \overrightarrow{RS}=\overrightarrow{0}$

Hence, assertion is true and reason is false