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