If P=3 i+√3 j+2 k and Q=4 i+√3 j+2.5 k then, the unit vector in the direction of P× Q is 1 x(√3 i+ j-2√3 k).… - JEE Main 2023 Physics PYQ

JEE Main 2023 — Physics Mechanics

2023integereasy

If $\vec{P}=3\hat{i}+\sqrt{3}\hat{j}+2\hat{k}$ and $\vec{Q}=4\hat{i}+\sqrt{3}\hat{j}+2.5\hat{k}$ then, the unit vector in the direction of $\vec{P}\times \vec{Q}$ is $\frac{1}{x}(\sqrt{3}\hat{i}+\hat{j}-2\sqrt{3}\hat{k})$ . The value of $x$ is

Official previous-year question

Held on 25 Jan 2023 · Verified 6 Jul 2026.

Did you get this right?

Solution

Unit vector in the direction of $\vec{P}\times \vec{Q}\text{is}\hat{n}=\frac{\vec{P}\times \vec{Q}}{|\vec{P}\times \vec{Q}|}$ .

Here, $\vec{P}\times \vec{Q}=|\begin{matrix}\hat{i} & \hat{j} & \hat{k} \\ 3 & \sqrt{3} & 2 \\ 4 & \sqrt{3} & 2.5\end{matrix}|=\sqrt{3}\frac{\hat{i}}{2}+\frac{\hat{j}}{2}-\sqrt{3}\hat{k}$

And $|\vec{P}\times \vec{Q}|=\sqrt{{(\frac{\sqrt{3}}{2})}^{2}+{(\frac{1}{2})}^{2}+{(\sqrt{3})}^{2}}=\sqrt{4}=2$

$\Rightarrow \frac{\vec{P}\times \vec{Q}}{|\vec{P}\times \vec{Q}|}=\frac{1}{2}(\sqrt{3}\frac{\hat{i}}{2}+\frac{\hat{j}}{2}-\sqrt{3}\hat{k})$

$=\frac{1}{4}(\sqrt{3}\hat{i}+\hat{j}-2\sqrt{3}\hat{k}) \Rightarrow x=4$

Your note

JEE Main Mechanics in other years

Mechanics 2026 Mechanics 2025 Mechanics 2024 Mechanics 2022 Mechanics 2021 Mechanics 2020 Mechanics 2019 Mechanics 2018 Mechanics 2017 Mechanics 2016 Mechanics 2015 Mechanics 2014

More JEE Main Mechanics questions

If $\epsilon, E$ and $t$ represent the free space permittivity, electric field and time respectively, then the unit of $\frac{\epsilon E}{t}$ will be :

2026easy

When a part of a straight capillary tube is placed vertically in a liquid, the liquid raises upto certain height $h$. If the inner radius of the capillary tube, density of the liquid and surface tension of the liquid decrease by $1 \%$ each, then the height of the liquid in the tube will change by $\%$.

2026medium

The velocity of a particle is given as $\vec{v} = -x\hat{i} + 2y\hat{j} - z\hat{k}$ m/s. The magnitude of acceleration at point $(1, 2, 4)$ is _______ m/s$^2$.

2026hard

Suppose there is a uniform circular disc of mass $M \mathrm{~kg}$ and radius $r \mathrm{~m}$ shown in figure. The shaded regions are cut out from the disc. The moment of inertia of the remainder about the axis $A$ of the disc is given by $\frac{x}{256} M r^{2}$. The value of $x$ is $\_\_\_\_$. ![JEE Main 2026 Physics, Rotational Motion — question figure](https://prepforbharat.s3.ap-south-1.amazonaws.com/exam/615f0e999476412f48314daf/Physics/images/Rotational_Motion/6983c19b8bfdbb24356396d6/question_1__q_6983c19b8bfdbb24356396d6__cdn-question-pool.getmarks.app__23S2_q_48_1__7376098484_final_ppt_sync.png)

2026hard

A soap bubble of surface tension $0.04 \mathrm{~N} / \mathrm{m}$ is blown to a diameter of 7 cm. If $(15000-x) \mu \mathrm{J}$ of work is done in blowing it further to make its diameter 14 cm, then the value of $x$ is $\_\_\_\_$. ($\pi=22 / 7$)

2026medium

View all Mechanics questions