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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
