Three particles P,Q and R are moving along the vectors A= i+ j, B= j+ k and C=- i+ j, respectively. They strike… - JEE Main 2021 Physics PYQ

JEE Main 2021 — Physics Mechanics

2021integermedium

Three particles $P,Q$ and $R$ are moving along the vectors $\vec{A}=\hat{i}+\hat{j},\vec{B}=\hat{j}+\hat{k}$ and $\vec{C}=-\hat{i}+\hat{j}$ , respectively. They strike on a point and start to move in different directions. Now particle $P$ is moving normal to the plane which contains vector $\vec{A}$ and $\vec{B}.$ Similarly particle $Q$ is moving normal to the plane which contains vector $\vec{A}$ and $\vec{C}.$ The angle between the direction of motion of $P$ and $Q$ is ${\mathrm{cos}}^{-1}(\frac{1}{\sqrt{x}}).$ Then the value of $x$ is $.$

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Held on 22 Jul 2021 · Verified 6 Jul 2026.

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Solution

Direction of $P,{\hat{v}}_{1}=\pm \frac{\vec{A}\times \vec{B}}{|\vec{A}\times \vec{B}|}=\pm \frac{\hat{i}-\hat{j}+\hat{k}}{\sqrt{3}}$

Direction of $Q,{\hat{v}}_{2}=\pm \frac{\vec{A}\times \vec{C}}{|\vec{A}\times \vec{C}|}=\pm \frac{2\hat{k}}{2}=\pm \hat{k}$

Angle between ${\hat{v}}_{1}$ and ${\hat{v}}_{2}$ ,

$\frac{{\hat{v}}_{1}\cdot {\hat{v}}_{2}}{|{\hat{v}}_{1}||{\hat{v}}_{2}|}=\frac{\pm \frac{1}{\sqrt{3}}}{(1)(1)}=\pm \frac{1}{\sqrt{3}}$

$\Rightarrow x=3$

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