Question

Assertion :The resultant of the three vector $\overrightarrow{OA},\overrightarrow{OB}$ and $\overrightarrow{OC}$ as shown in the figure is $R(1+\sqrt{2})$.Here $R$ is the radius of the circle.(Here $\angle AOB=\angle BOC={45}^{\circ }$) Reason: $\overrightarrow{OA}+\overrightarrow{OC}$ is along $\overrightarrow{OB}$ and $(\overrightarrow{OA}+\overrightarrow{OC})+\overrightarrow{OB}$ is along $\overrightarrow{OB}$

• 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 A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

The magnitude of all the vectors is $R$.

Magnitude resultant vector of two same magnitude vectors eith angle of ${45}^0$ is $\sqrt{2}R$

Because $(\overrightarrow{OA}+\overrightarrow{OC})$ and $\overrightarrow{OB}$ are along the same direction only magnitudes are to be added.