Three vectors overrightarrow OP , overrightarrow OQ and overrightarrow OR each of magnitude A are acting as shown in figure. The resultant of the three vectors is A √(x) . The value of x is

Physics · Vectors and Scalars

JEE Main 2024 — 8 April, Shift 1 — Question 55

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 $\qquad$

Answer: 3

Numerical answer — enter this value.

Step-by-step solution

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

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

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 8 April, Shift 1
Subject: Physics
Chapter: Vectors and Scalars
Topic: Properties and addition/Subtraction of Vectors