Question

Assertion :In $\Delta$ABC, $\overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{CA}=0$ Reason: If $\overrightarrow{OA}=\overrightarrow{a},\overrightarrow{OB}=\overrightarrow{b}$, then $\overrightarrow{AB}=\overrightarrow{a}+\overrightarrow{b}$

• 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. Assertion is incorrect but Reason is correct

Answer 1

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

In $\Delta ABC,\overrightarrow{AB}+\overrightarrow{BC}=\overrightarrow{AC}=-\overrightarrow{CA}$
or $\overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{CA}=\overrightarrow{O}$
$\overrightarrow{OA}+\overrightarrow{AB}=\overrightarrow{OB}$ is the triangle law of addition.

But, if $\overrightarrow{OA}=\overrightarrow{a}$ and $\overrightarrow{OB}=\overrightarrow{b}$, then $\overrightarrow{AB}=\overrightarrow{b}-\overrightarrow{a}$

Hence, Statement $1$ is true and Statement $2$ is false.