Vector Algebra — JEE Main Mathematics Previous Year Questions

How many JEE Main questions come from Vector Algebra?

Vector Algebra has contributed 198 questions to Joint Entrance Examination (Main) papers between 2016 and 2026 — an average of about 18 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 198 questions carries a written, step-by-step solution, and each is tagged to Vector Algebra within Mathematics, 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 198 Vector Algebra questions (with full written solutions) are available in practice.

1. Question 1 · JEE Main 2026

   If $\vec{a}$ and $\vec{b}$ are two vectors such that $|\vec{a}|=2$ and $|\vec{b}|=3$, then the maximum value of $3|(3\vec{a}+2\vec{b})|+4|(3\vec{a}-2\vec{b})|$ is :
   1. (A)30
   2. (B)36
   3. (C)60
   4. (D)72
   Show answerAnswer

   Answer: (C) 60

2. Question 2 · JEE Main 2026

   For three unit vectors $\vec{a},\vec{b},\vec{c}$ satisfying $|\vec{a}-\vec{b}{|}^2+|\vec{b}-\vec{c}{|}^2+|\vec{c}-\vec{a}{|}^2=9\text{ and }|2\vec{a}+k\vec{b}+k\vec{c}|=3\text{, }$ the positive value of k is :
   1. (A)4
   2. (B)5
   3. (C)6
   4. (D)3
   Show answerAnswer

   Answer: (B) 5

3. Question 3 · JEE Main 2026

   Let $\hat{u}$ and $\hat{v}$ be unit vectors inclined at an acute angle such that $|\hat{u}\times \hat{v}|=\frac{\sqrt{3}}{2}$. If $\overrightarrow{\mathrm{A}}=\lambda \hat{u}+\hat{v}+(\hat{u}\times \hat{v})$, then $\lambda$ is equal to:
   1. (A)$$\frac{4}{3}(\overrightarrow{\mathrm{A}}\cdot \hat{u})-\frac{2}{3}(\overrightarrow{\mathrm{A}}\cdot \hat{v})$$
   2. (B)$$\frac{2}{3}(\overrightarrow{\mathrm{A}}\cdot \hat{u})-\frac{1}{3}(\overrightarrow{\mathrm{A}}\cdot \hat{v})$$
   3. (C)$$\frac{4}{3}(\overrightarrow{\mathrm{A}}\cdot \hat{u})+\frac{2}{3}(\overrightarrow{\mathrm{A}}\cdot \hat{v})$$
   4. (D)$$(\overrightarrow{\mathrm{A}}\cdot \hat{u})-\frac{1}{2}(\overrightarrow{\mathrm{A}}\cdot \hat{v})$$
   Show answerAnswer

   Answer: (A) $\frac{4}{3}(\overrightarrow{\mathrm{A}}\cdot \hat{u})-\frac{2}{3}(\overrightarrow{\mathrm{A}}\cdot \hat{v})$

4. Question 4 · JEE Main 2026

   Let $\vec{a}=\sqrt{7}\hat{i}+\hat{j}-\hat{k}$ and $\vec{b}=\hat{j}+2\hat{k}$. If $\vec{r}$ is a vector such that $\vec{r}\times \vec{a}+\vec{a}\times \vec{b}=\overrightarrow{0}$ and $\vec{r}\cdot \vec{a}=0$, then $|3\vec{r}{|}^2$ is equal to:
   1. (A)44
   2. (B)54
   3. (C)86
   4. (D)132
   Show answerAnswer

   Answer: (A) 44

5. Question 5 · JEE Main 2026

   Let $\vec{a},\vec{b},\vec{c}$ be three vectors such that $\vec{a}\times \vec{b}=2(\vec{a}\times \vec{c})$. If $|\vec{a}|=1,|\vec{b}|=4,|\vec{c}|=2$, and the angle between $\vec{b}$ and $\vec{c}$ is $60^{\circ }$, then $|\vec{a}\cdot \vec{c}|$ is equal to
   1. (A)2
   2. (B)0
   3. (C)1
   4. (D)4
   Show answerAnswer

   Answer: (C) 1

Vector Algebra questions by year

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