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Vector- JEE Advanced Previous Year Questions with Solutions

This Vector chapter summary covers JEE Advanced problems on vector algebra, position vectors, vector addition, proportional division of line segments, and applications of vectors in physical systems such as expanding spheres and density changes.

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Vector- JEE Advanced Previous Year Questions with Solutions

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JEE Advanced Previous Year Questions of Physics with Solutions are available at eSaral. Practicing JEE Advanced Previous Year Papers Questions of Physics will help the JEE aspirants in realizing the question pattern as well as help in analyzing weak & strong areas. Get detailed Class 11th & 12th Physics Notes to prepare for Boards as well as competitive exams like IIT JEE, NEET etc. eSaral helps the students in clearing and understanding each topic in a better way. eSaral is providing complete chapter-wise notes of Class 11th and 12th both for all subjects.     Click Here for JEE main Previous Year Topic Wise Questions of Physics with Solutions    Download eSaral app  for free study material and video tutorials.     Simulator   Previous Years JEE Advanced Questions

Q. Three vectors $\overrightarrow{\mathrm{P}}, \overrightarrow{\mathrm{Q}}$ and $\overrightarrow{\mathrm{R}}$ are shown in the figure. Let S be any point on the vector $\overrightarrow{\mathrm{R}}$. The distance between the points P and S is b $|\overrightarrow{\mathrm{R}}|$. The general relation among vectors $\overrightarrow{\mathrm{P}}, \overrightarrow{\mathrm{Q}}$ and $\overrightarrow{\mathrm{S}}$ is : $(\mathrm{A}) \overrightarrow{\mathrm{S}}=(1-\mathrm{b}) \overrightarrow{\mathrm{P}}+\mathrm{b}^{2} \overrightarrow{\mathrm{Q}}$ (B) $\overrightarrow{\mathrm{S}}=(b-1) \overrightarrow{\mathrm{P}}+b \overrightarrow{\mathrm{Q}}$ (C) $\overrightarrow{\mathrm{S}}=(1-\mathrm{b}) \overrightarrow{\mathrm{P}}+\mathrm{b} \overrightarrow{\mathrm{Q}}$ $(\mathrm{D}) \overrightarrow{\mathrm{S}}=\left(1-\mathrm{b}^{2}\right) \overrightarrow{\mathrm{P}}+\mathrm{b} \overrightarrow{\mathrm{Q}}$ [JEE Advanced - 2017]
Ans. (C) Let vector from point P to point S be $\overrightarrow{\mathrm{c}}$ $\Rightarrow \overrightarrow{\mathrm{c}}=\mathrm{b}|\overrightarrow{\mathrm{R}}| \hat{\mathrm{R}}=\mathrm{b}|\overrightarrow{\mathrm{R}}|\left(\frac{\overrightarrow{\mathrm{R}}}{|\overrightarrow{\mathrm{R}}|}\right)=\mathrm{b} \overrightarrow{\mathrm{R}}=\mathrm{b}(\overrightarrow{\mathrm{Q}}-\overrightarrow{\mathrm{P}})$ from triangle rule of vector addition $\overrightarrow{\mathrm{P}}+\overrightarrow{\mathrm{C}}=\overrightarrow{\mathrm{S}}$ $\overrightarrow{\mathrm{P}}+\mathrm{b}(\overrightarrow{\mathrm{Q}}-\overrightarrow{\mathrm{P}})=\overrightarrow{\mathrm{S}}$ $\Rightarrow \overrightarrow{\mathrm{S}}=(1-\mathrm{b}) \overrightarrow{\mathrm{P}}+\mathrm{b} \overrightarrow{\mathrm{Q}}$
Q. Consider an expanding sphere of instantaneous radius R whose total mass remains constant. The expansion is such that the instantaneous density  remains uniform throughout the volume. The rate of fractional change in density $\left(\frac{1}{\rho} \frac{\mathrm{d} \rho}{\mathrm{dt}}\right)$ is constant. The velocity v of any point on the surface of the expanding sphere is proportional to : (A) $\mathrm{R}^{3}$ (B) $\frac{1}{\mathrm{R}}$ (C) R (D) $\mathrm{R}^{2 / 3}$ [JEE Advanced - 2017]
Ans. (C) Density of sphere is $\rho=\frac{\mathrm{m}}{\mathrm{v}}=\frac{3 \mathrm{m}}{4 \pi \mathrm{R}^{3}}$ $\Rightarrow \frac{1}{\rho} \frac{\mathrm{d} \rho}{\mathrm{dt}}=-\frac{3}{\mathrm{R}} \frac{\mathrm{d} \mathrm{R}}{\mathrm{dt}}$ since $\Rightarrow \frac{1}{\rho} \frac{\mathrm{d} \rho}{\mathrm{dt}}$ is constant $\therefore \frac{\mathrm{d} \mathrm{R}}{\mathrm{dt}} \propto \mathrm{R}$ Velocity of any point on the circumfrence V is equal to $\frac{\mathrm{d} \mathrm{R}}{\mathrm{dt}}$ (rate of change of radius of outer layer)

Frequently Asked Questions

Find answers to common questions.

How many vector questions come in JEE Advanced each year?

Typically 1–2 dedicated vector questions appear per JEE Advanced paper. However, vector operations appear implicitly in 40–50% of Physics questions across Mechanics, Electromagnetism, and Optics. Mastering vectors therefore has a multiplier effect on your total Physics score.

Is the section formula important for JEE Advanced vectors?

Yes. The 2017 question directly tested the section formula in vector form — $\vec{S} = (1-b)\vec{P} + b\vec{Q}$. This result connects position vectors to coordinate geometry and appears in both Physics and Mathematics papers. Understanding its derivation (not just memorising it) is essential.

What is the difference between dot product and cross product in JEE Advanced problems?

The dot product gives a scalar result and is used for work, projection, and angle between vectors. The cross product gives a vector result (perpendicular to both) and is used for torque, angular momentum, and magnetic force. JEE Advanced tests both, but cross product questions tend to be harder because direction matters.

Can vectors questions appear in Mathematics paper of JEE Advanced too?

Yes. The JEE Advanced Mathematics paper (Paper 1 and Paper 2) includes a dedicated chapter on Vector Algebra and 3D Geometry, which is separate from Physics vectors. These questions test dot products, cross products, planes, and lines in 3D. Practice both papers for full coverage.

How do I avoid sign errors in vector differentiation problems?

Write the fractional rate expression explicitly before substituting: $\frac{1}{f}\frac{df}{dt} = k$. Then differentiate the relevant physical quantity (volume, density, radius) step by step, keeping track of negative signs from the chain rule. Rushing to substitute directly into a formula is the most common source of errors in this question type.

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Comments

Abhishek Verma
March 16, 2026, 10:07 p.m.
Thank you so much very good questions.
Deep Bhati
July 12, 2024, 2:22 p.m.
Very best questions
Anurag tiwari
July 2, 2021, 8:11 p.m.
E Saral is best app for iit jee
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