If two vectors $$\vec{A}$$ and $$\vec{B}$$ having equal magnitude $$R$$ are inclined at angle $$\theta$$, then

$$|\vec{A}+\vec{B}|=2 R \cos \left(\frac{\theta}{2}\right)$$

$$|\vec{A}-\vec{B}|=2 R \cos \left(\frac{\theta}{2}\right)$$

$$|\vec{A}-\vec{B}|=\sqrt{2} R \sin \left(\frac{\theta}{2}\right)$$

$$|\vec{A}+\vec{B}|=2 R \sin \left(\frac{\theta}{2}\right)$$

The angle between vector $$\vec{Q}$$ and the resultant of $$(2 \vec{Q}+2 \vec{P})$$ and $$(2 \vec{Q}-2 \vec{P})$$ is :

$$ \tan ^{-1}(\mathrm{P} / \mathrm{Q}) $$

$$ \tan ^{-1} \frac{(2 \vec{Q}-2 \vec{P})}{2 \vec{Q}+2 \vec{P}} $$

$$ \tan ^{-1}(2 Q / \mathrm{P}) $$

Vector Algebra — JEE Main Physics Previous Year Questions

38 solved PYQs · 2018–2026 · Physics

Solved PYQs: 38
Years covered: 2018–2026
Avg / year: ~4
Subject: Physics

How many JEE Main questions come from Vector Algebra?

Vector Algebra has contributed 38 questions to Joint Entrance Examination (Main) papers between 2018 and 2026 — an average of about 4 questions a year. That count is measured from EByAi’s bank of 55,289 JEE Main questions, not estimated from a syllabus. Every one of the 38 questions carries a written, step-by-step solution, and each is tagged to Vector Algebra within Physics, so you can drill this chapter across every year at once instead of hunting through paper PDFs. Practising a chapter’s full PYQ history is the fastest way to learn the patterns examiners reuse.

Sample Vector Algebra questions from real JEE Main papers

These are 5 real questions from the bank — exactly as asked, with the answer one tap away. All 38 Vector Algebra questions (with full written solutions) are available in practice.

Question 1 · JEE Main 2026
The velocity of a particle is given as $v = - x \hat{i} + 2 y \hat{j} - z \hat{k}$ m/s. The magnitude of acceleration at point (1, 2, 4) is ________ m/s 2 .
1. (A) $6$
2. (B) $9$
3. (C) $33$
4. (D) $0$
Show answerAnswer
$Answer: (B) 9$
Question 2 · JEE Main 2024
If two vectors $A$ and $B$ having equal magnitude $R$ are inclined at angle $θ$ , then
1. (A) $∣ A + B ∣ = 2 R cos (\frac{θ}{2})$
2. (B) $∣ A - B ∣ = 2 R cos (\frac{θ}{2})$
3. (C) $∣ A - B ∣ = 2 R sin (\frac{θ}{2})$
4. (D) $∣ A + B ∣ = 2 R sin (\frac{θ}{2})$
Show answerAnswer
$Answer: (A) ∣ A + B ∣ = 2 R cos (\frac{θ}{2})$
Question 3 · JEE Main 2024
The angle between vector $Q$ and the resultant of $(2 Q + 2 P)$ and $(2 Q - 2 P)$ is :
1. (A) $tan^{- 1} (P / Q)$
2. (B) $0^{\circ}$
3. (C) $tan^{- 1} \frac{( 2 Q - 2 P )}{2 Q + 2 P}$
4. (D) $tan^{- 1} (2 Q / P)$
Show answerAnswer
$Answer: (B) 0^{\circ}$
Question 4 · JEE Main 2023
Two forces having magnitude $A$ and $\frac{A}{2}$ are perpendicular to each other. The magnitude of their resultant is:
1. (A) $\frac{5 A}{2}$
2. (B) $\frac{5 A}{4}$
3. (C) $\frac{5 A}{2}$
4. (D) $\frac{5 A ^{2}}{2}$
Show answerAnswer
$Answer: (C) \frac{5 A}{2}$
Question 5 · JEE Main 2023
If two vectors $P = i + 2 m j + m k$ and $Q = 4 i - 2 j + m k$ are perpendicular to each other. Then, the value of m will be :
1. (A) $- 1$
2. (B) $3$
3. (C) $1$
4. (D) $2$
Show answerAnswer
$Answer: (D) 2$

Vector Algebra questions by year

Year	Questions	Share of chapter questions
2026	1
2025	1
2024	7
2023	6
2022	5
2021	13
2020	1
2019	3
2018	1

Practise these 38 questions with solutions

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FAQs

How many JEE Main questions have been asked from Vector Algebra?

EByAi's bank holds 38 real JEE Main questions from Vector Algebra, asked between 2018 and 2026 — about 4 per year on average. Every count is measured from actual papers, not estimated.

Is Vector Algebra important for JEE Main?

38 questions over 9 papers make Vector Algebra a steady-weightage chapter in JEE Main Physics. The year-wise table above shows exactly how often it appears.

Can I solve Vector Algebra PYQs online for free?

Yes. EByAi lets you solve JEE Main past-year questions in the browser with written solutions — free daily practice, no card needed.

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