Q 11-03-071JEE MainJEE Main 2024 (8 Apr, Shift 1)Easy
Three vectors $\overrightarrow{OP}$, $\overrightarrow{OQ}$ and $\overrightarrow{OR}$, each of magnitude $A$, are acting as shown in the figure. The resultant of the three vectors is $A\sqrt x$. The value of $x$ is ______.
Numerical value type. Enter your answer.
Answer: 3
Take $\overrightarrow{OP}$ along $+x$ and $\overrightarrow{OQ}$ along $+y$. $\overrightarrow{OR}$ is $45^\circ$ below $+x$.
$$R_x = A + A\cos45^\circ = A\left(1 + \frac{1}{\sqrt2}\right),\qquad R_y = A - A\sin45^\circ = A\left(1 - \frac{1}{\sqrt2}\right)$$
$$R^2 = A^2\left[\left(1 + \frac{1}{\sqrt2}\right)^2 + \left(1 - \frac{1}{\sqrt2}\right)^2\right] = A^2\left(2 + 1\right) = 3A^2$$
So $R = A\sqrt3$ and $x = 3$.
Solution by Sreeraj P, M.Sc Physics