Question

Magnitude of resultant of $3$ vectors $\overrightarrow{OA},\overrightarrow{OB}$, and $\overrightarrow{OC}$ as shown below is

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

Answer 1

The correct option is C $r(1+\sqrt{2})$

$\overrightarrow{OA}$ and $\overrightarrow{OC}$ are equal in magnitude and inclined to each other at an angle $90°$. So their resultant is $\sqrt{2}r$, and it acts along $\overrightarrow{OB}$. So,
Resultant $=r+\sqrt{2}r$
$=r(1+\sqrt{2})$