Vectors JEE Main PYQs PDF, 2020–2026

Vectors has 216 questions in JEE Main papers from 2020 to 2026, about 31 per year across all shifts. The free PDF has 212 of them, each with its answer. The most asked topic is Dot and Cross Product (160 questions), followed by Scalar Triple Product (18) and Coplanarity and Collinearity (17).

Asked in JEE Main: 2162020–2026, all shifts
In this free PDF: 212with answers
Asked in 2026: 24Latest paper: 2026 Apr S2
Most asked topic: Dot and Cross Product160 Qs · 74% of the chapter
Difficulty mix: 5% easy · 86% medium · 9% hardof the questions in the PDF

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Source: official NTA JEE Main papers · Updated 25 Oct 2026

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13 of this chapter's questions came back in a later paper (2021–2026). See the most repeated.

How often it's asked in JEE Main

Vectors had about 1.5 questions per shift in recent JEE Main papers (2024–26). It's one of the most asked Mathematics chapters. Most asked topic: Dot and Cross Product. About 24 questions in the 2026 papers. (Some topics were cut in 2024; see what changed.)

It came up in almost every 2024–26 shift in our bank (about 57 shifts). Question types in 2020–2026: about 160 MCQs and about 56 numerical.

How many questions from Vectors in JEE Main, year by year

Year	Questions	Per shift	MCQ	Numerical
2026	24	1.3	21	3
2025	23	1.2	18	5
2024	40	2.0	31	9
2023	46	1.9	37	9
2022	31	1.3	25	6
2021	37	1.4	21	16
2020	15	0.9	7	8
2020–2026	216	1.5	160	56

Most asked Vectors topics, 2020–2026

Topic	Questions
Dot and Cross Product	160
Scalar Triple Product	18
Coplanarity and Collinearity	17
Types of Vectors	10
Vector Triple Product	10

Every topic, year by year, is in the topic-wise table further down.

Counted from PrepWiser's question bank of JEE Main papers, 2020–2026. Per shift = questions that year ÷ shifts in our bank. Updated 25 Oct 2026.

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Two free sheets, made from the past JEE Main questions on this chapter.

Revision notes10 pages, 24 ideas with the usual mistakes.Open the revision notes Formula sheet3 pages, all 25 formulas.Open the formula sheet

Vectors questions per year

Year	Asked	In PDF
2026	24	22
2025	23	23
2024	40	40
2023	46	46
2022	31	30
2021	37	37
2020	15	14

in the free PDF asked, not in the PDFThe PDF only has questions we can print in full with a checked answer, so it holds 212 of the 216 asked.

Topic-wise weightage by year

How many Vectors questions each topic had in every JEE Main year (all shifts), counting every question asked, including ones not in the PDF. Darker cells mean more questions.

Topic	Asked	Share	2026	2025	2024	2023	2022	2021	2020
Dot and Cross Product	160	74%	20	20	35	31	22	23	9
Scalar Triple Product	18	8%	·	1	1	4	2	6	4
Coplanarity and Collinearity	17	8%	·	1	2	8	3	3	·
Types of Vectors	10	5%	2	1	1	2	1	2	1
Vector Triple Product	10	5%	2	·	·	1	3	3	1
Vector Equation of Line	1	0%	·	·	1	·	·	·	·
All topics	216	100%	24	23	40	46	31	37	15

Swipe the table sideways for older years.

Newest questions (2026)

The 12 newest of the 22 JEE Main 2026 Vectors questions in the free PDF, latest shift first. The 2026 papers asked 24 in all.

JEE Main 2026 · 8 Apr · Shift 2 · Dot and Cross Product

Let $\overrightarrow{{\mathrm{a}}}=4{\hat{i}}-{\hat{j}}+3{\hat{k}},\overrightarrow{{\ \mathrm{b}}}=10{\hat{i}}+2{\hat{j}}-{\hat{k}}$ and a vector $\overrightarrow{{\mathrm{c}}}$ be such that $2(\overrightarrow{{\mathrm{a}}}\times \overrightarrow{{\mathrm{b}}})+3(\overrightarrow{{\ \mathrm{b}}}\times \overrightarrow{{\mathrm{c}}})=\vec{0}$ .

If $\overrightarrow{{\mathrm{a}}}\cdot \overrightarrow{{\mathrm{c}}}=15$ , then $\overrightarrow{{\mathrm{c}}}\cdot ({\hat{i}}+{\hat{j}}-3{\hat{k}})$ is equal to :

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JEE Main 2026 · 6 Apr · Shift 1 · Vector Triple Product

If ${\vec{a}}={\hat{i}}+{\hat{j}}+{\hat{k}},{\vec{b}}={\hat{j}}-{\hat{k}}$ and ${\vec{c}}$ be three vectors such that ${\vec{a}}\times {\vec{c}}={\vec{b}}$ and ${\vec{a}}\cdot {\vec{c}}=3$ , then ${\vec{c}}\cdot ({\vec{a}}-2{\vec{b}})$ is equal to $\_\_\_\_$ .
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JEE Main 2026 · 6 Apr · Shift 2 · Dot and Cross Product

Let $\overrightarrow{{\mathrm{a}}}=2{\hat{i}}+3{\hat{j}}+3{\hat{k}}$ and $\overrightarrow{{\mathrm{b}}}=6{\hat{i}}+3{\hat{j}}+3{\hat{k}}$ . Then the square of the area of the triangle with adjacent sides determined by the vectors $(2{\vec{a}}+3{\vec{b}})$ and $({\vec{a}}-{\vec{b}})$ is :

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JEE Main 2026 · 5 Apr · Shift 1 · Dot and Cross Product

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 ${\vec{r}}\times {\vec{a}}+{\vec{a}}\times {\vec{b}}=\vec{0}$ and ${\vec{r}}\cdot {\vec{a}}=0$ , then $|3{\vec{r}}|^{2}$ is equal to:

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JEE Main 2026 · 5 Apr · Shift 2 · Types of Vectors

Let $O$ be the origin, $\overrightarrow{OP}={\vec{a}}$ and $\overrightarrow{OQ}={\vec{b}}$ . If $R$ is the point on $\overrightarrow{OP}$ such that $\overrightarrow{OP}=5\overrightarrow{OR}$ , and $M$ is the point such that $\overrightarrow{OQ}=5\overrightarrow{RM}$ , then $\overrightarrow{PM}$ is equal to :

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JEE Main 2026 · 4 Apr · Shift 2 · Dot and Cross Product

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:
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JEE Main 2026 · 2 Apr · Shift 2 · Dot and Cross Product

Two adjacent sides of a parallelogram PQRS are given by $\overrightarrow{PQ}={\hat{j}}+{\hat{k}}$ and $\overrightarrow{PS}={\hat{i}}-{\hat{j}}$ . If the side PS is rotated about the point P by an acute angle $\alpha$ in the plane of the parallelogram so that it becomes perpendicular to the side PQ, then $\sin^{2}\left(\frac{5\alpha}{2}\right)-\sin^{2}\left(\frac{\alpha}{2}\right)$ is equal to:
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JEE Main 2026 · 2 Apr · Shift 2 · Dot and Cross Product

Let the vectors ${\vec{a}}=-{\hat{i}}+{\hat{j}}+3{\hat{k}}$ and ${\vec{b}}={\hat{i}}+3{\hat{j}}+{\hat{k}}$ . For some $\lambda,\mu\in {\mathbb{R}}$ , let ${\vec{c}}=\lambda{\vec{a}}+\mu{\vec{b}}$ .
If ${\vec{c}}\cdot (3{\hat{i}}-6{\hat{j}}+2{\hat{k}})=10$ and ${\vec{c}}\cdot ({\hat{i}}+{\hat{j}}+{\hat{k}})=-2$ , then $|{\vec{c}}|^{2}$ is equal to :
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JEE Main 2026 · 2 Apr · Shift 1 · Dot and Cross Product

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 :
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JEE Main 2026 · 28 Jan · Shift 1 · Dot and Cross Product

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 :

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JEE Main 2026 · 28 Jan · Shift 2 · Dot and Cross Product

Let P be a point in the plane of the vectors $\overrightarrow{AB}=3{\hat{i}}+{\hat{j}}-{\hat{k}}$ and $\overrightarrow{AC}={\hat{i}}-{\hat{j}}+3{\hat{k}}$ such that P is equidistant from the lines AB and AC. If $|\overrightarrow{AP}|=\frac{\sqrt{5}}{2}$ , then the area of the triangle ABP is :
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JEE Main 2026 · 24 Jan · Shift 1 · Dot and Cross Product

Let ${\vec{a}}=2{\widehat{{\mathrm{i}}}}+{\widehat{{\mathrm{j}}}}-2{\widehat{{\mathrm{k}}}},{\vec{b}}={\widehat{{\mathrm{i}}}}+{\widehat{{\mathrm{j}}}}$ and ${\vec{c}}={\vec{a}}\times {\vec{b}}$ . Let ${\vec{d}}$ be a vector such that $|{\vec{d}}-{\vec{a}}|=\sqrt{11},|{\vec{c}}\times {\vec{d}}|=3$ and the angle between ${\vec{c}}$ and ${\vec{d}}$ is $\frac{\pi}{4}$ . Then ${\vec{a}}\cdot {\vec{d}}$ is equal to

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Sample questions from recent papers

JEE Main 2026 · 23 Jan · Shift 1 · Vector Triple Product

Let $\overrightarrow{{\mathrm{a}}}=-{\hat{i}}+{\hat{j}}+2{\hat{k}},\overrightarrow{{\ \mathrm{b}}}={\hat{i}}-{\hat{j}}-3{\hat{k}},\overrightarrow{{\mathrm{c}}}=\overrightarrow{{\mathrm{a}}}\times \overrightarrow{{\mathrm{b}}}$ and $\overrightarrow{{\mathrm{d}}}=\overrightarrow{{\mathrm{c}}}\times \overrightarrow{{\mathrm{a}}}$ . Then $({\vec{a}}-{\vec{b}})\cdot {\vec{d}}$ is equal to :

(A)
2
(B)
-2
(C)
4
(D)
-4

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Answer: (B)

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JEE Main 2025 · 24 Jan · Shift 2 · Types of Vectors

Let the position vectors of three vertices of a triangle be $4 \vec{p}+\vec{q}-3 \vec{r},-5 \vec{p}+\vec{q}+2 \vec{r}$ and $2 \vec{p}-\vec{q}+2 \vec{r}$ . If the position vectors of the orthocenter and the circumcenter of the triangle are $\frac{\vec{p}+\vec{q}+\vec{r}}{4}$ and $\alpha \vec{p}+\beta \vec{q}+\gamma \vec{r}$ respectively, then $\alpha+2 \beta+5 \gamma$ is equal to :

(A)4
(B)3
(C)1
(D)6

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Answer: (B)

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JEE Main 2025 · 23 Jan · Shift 1 · Scalar Triple Product

Let the position vectors of the vertices $\mathrm{A}, \mathrm{B}$ and C of a tetrahedron ABCD be $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathrm{k}}, \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-2 \hat{k}$ and $2 \hat{i}+\hat{j}-\hat{k}$ respectively. The altitude from the vertex $D$ to the opposite face $A B C$ meets the median line segment through $A$ of the triangle $A B C$ at the point $E$ . If the length of $A D$ is $\frac{\sqrt{110}}{3}$ and the volume of the tetrahedron is $\frac{\sqrt{805}}{6 \sqrt{2}}$ , then the position vector of E is

(A) $\frac{1}{6}(7 \hat{\mathrm{i}}+12 \hat{\mathrm{j}}+\hat{\mathrm{k}})$
(B) $\frac{1}{12}(7 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}+3 \hat{\mathrm{k}})$
(C) $\frac{1}{6}(12 \hat{i}+12 \hat{j}+\hat{k})$
(D) $\frac{1}{2}(\hat{i}+4 \hat{j}+7 \hat{k})$

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Answer: (A)

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JEE Main 2025 · 23 Jan · Shift 1 · Coplanarity and Collinearity

Let the arc $A C$ of a circle subtend a right angle at the centre $O$ . If the point $B$ on the arc $A C$ , divides the arc $A C$ such that $\frac{\text { length of } \operatorname{arc} A B}{\text { length of } \operatorname{arc} B C}=\frac{1}{5}$ , and $\overrightarrow{O C}=\alpha \overrightarrow{O A}+\beta \overrightarrow{O B}$ , then $\alpha+\sqrt{2}(\sqrt{3}-1) \beta$ is equal to

(A) $2 \sqrt{3}$
(B) $5 \sqrt{3}$
(C) $2+\sqrt{3}$
(D) $2-\sqrt{3}$

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Answer: (D)

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JEE Main 2024 · 30 Jan · Shift 2 · Vector Equation of Line

Let $L_1: \vec{r}=(\hat{i}-\hat{j}+2 \hat{k})+\lambda(\hat{i}-\hat{j}+2 \hat{k}), \lambda \in \mathbb{R}$ ,

$L_2: \vec{r}=(\hat{j}-\hat{k})+\mu(3 \hat{i}+\hat{j}+p \hat{k}), \mu \in \mathbb{R} \text {, and } L_3: \vec{r}=\delta(\ell \hat{i}+m \hat{j}+n \hat{k}), \delta \in \mathbb{R}$

be three lines such that $L_1$ is perpendicular to $L_2$ and $L_3$ is perpendicular to both $L_1$ and $L_2$ . Then, the point which lies on $L_3$ is

(A) $(1,7,-4)$
(B) $(1,-7,4)$
(C) $(-1,7,4)$
(D) $(-, 1-7,4)$

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Answer: (C)

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Frequently asked

How many questions come from Vectors in JEE Main?

216 questions from 2020 to 2026, about 31 per year. In 2026 it had 24. The free PDF has 212 of them.

Which Vectors topics are most important for JEE Main?

By past papers: Dot and Cross Product (74%), Scalar Triple Product (8%) and Coplanarity and Collinearity (8%) of all Vectors questions.

Is the Vectors PYQ PDF free?

Yes. The PDF and its answer key are free, and you can practise the questions online with no login, with step-by-step solutions where available.

Prefer to solve online? Practise Vectors online with step-by-step solutions where available, or work through JEE Main papers shift by shift.

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JEE Main PYQs by year: 2026 · 2025 · 2024 · 2023 · 2022 · 2021 · 2020

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Answers follow NTA's final answer keys. Typing errors are possible, so check doubtful answers against the official key. Spotted a mistake? prepwiser.in/feedback · Terms: prepwiser.in/terms

Vectors JEE Main PYQs PDF, 2020–2026

How often it's asked in JEE Main

How many questions from Vectors in JEE Main, year by year

Most asked Vectors topics, 2020–2026

Revise Vectors before you practise

Send this chapter to your study group

Vectors questions per year

Topic-wise weightage by year

Newest questions (2026)

Sample questions from recent papers

Practise these online, free, no login

Frequently asked

How many questions come from Vectors in JEE Main?

Which Vectors topics are most important for JEE Main?

Is the Vectors PYQ PDF free?

More Mathematics chapters