Question 7 of 121

Three vectors $\overrightarrow{\mathrm{OP}}, \overrightarrow{\mathrm{OQ}}$ and $\overrightarrow{\mathrm{OR}}$ each of magnitude $\mathrm{A}$ are acting as shown in figure. The resultant of the three vectors is $\mathrm{A} \sqrt{x}$. The value of $x$ is ________ .

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Answer: 3

$\begin{aligned} & \vec{R}=\left(A+\frac{A}{\sqrt{2}}\right) \hat{i}+\left(A-\frac{A}{\sqrt{2}}\right) \hat{j} \\ & |\vec{R}|=\sqrt{\left(A+\frac{A}{\sqrt{2}}\right)^2+\left(A-\frac{A}{\sqrt{2}}\right)^2}=\sqrt{3} A\end{aligned}$