Three vectors $\overrightarrow{O P}, \overrightarrow{O Q}$ and $\overrightarrow{O R}$ each of magnit

Question

Three vectors $\overrightarrow{O P}, \overrightarrow{O Q}$ and $\overrightarrow{O R}$ 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\

Professor PC Thomas Classes · Answer

(3) :\ } Since $\overrightarrow{O P}$ and $\overrightarrow{O Q}$ are perpendicular to each other, resultant of $\overrightarrow{O P}$ and $\overrightarrow{O Q}$ is $\sqrt{2} A$. Resultant of three vectors, $$ R=\sqrt{(\sqrt{2} A)^{2}+A^{2}}=\sqrt{3 A^{2}}=A \sqrt{3} $$