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

Question

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 _______.

Answer 1

Correct answer is : 3 

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

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