Three vectors overrightarrow{mathrm{OP}}, overrightarrow{mathrm{OQ}} and overrightarrow{mathrm{OR}}

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3-1.Vectors

hard

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

A

$5$

B

$4$

C

$2$

D

$3$

(JEE MAIN-2024)

Solution

$\vec{R}=\left(A+\frac{A}{\sqrt{2}}\right) \hat{i}+\left(A-\frac{A}{\sqrt{2}}\right) \hat{j}$

$|\vec{R}|=\sqrt{\left(A+\frac{A}{\sqrt{2}}\right)^2+\left(A-\frac{A}{\sqrt{2}}\right)^2}=\sqrt{3} A$

Standard 11

Physics

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