Question

Find the resultant of three vectors shown in figure. Radius of circle is R:

• A. $R(1+\sqrt{2})$
• B. $R(\sqrt{2}-1)$
• C. $R^2(\sqrt{2}-1)$
• D. $R(\sqrt{3}-\sqrt{2})$

Answer 1

Answer: (A)

OA $=OC$
$\overrightarrow{OA}+\overrightarrow{OC}$ is along
$\overrightarrow{OB}$, and its magnitude is
$2R\cos 45=R\sqrt{2}$
$(\overrightarrow{OA}+\overrightarrow{OC})+\overrightarrow{OB}$ is along
$\overrightarrow{OB}$ and its magnitude is
$\sqrt{2}R+R=R(\sqrt{2}+1)$