JEE Main · Maths · Vector Algebra
Dot Product: JEE Main previous year questions
36 questions in the 108 JEE Main shifts Lumi analysed, in 7 of 8 years. Pattern: Asked most years. 15 came in 2024–26. Here is how it is asked and which ideas come back.
- Questions
- 36
- in 33 of 108 shifts
- Years asked
- 7/8
- last asked 2026
- Weighted estimate
- 0.3
- model; history: 0.3 a shift on average, typically 0.1–0.4
Key findings
- 01
Asked in 7 of 8 years with analysed shifts and in 33 of 108 shifts: 36 questions, #91 of 196 topics.
- 02
44% of its questions since 2020 tested an idea no earlier year had asked; 11 repeated an idea from the year before.
- 03
The most repeated idea is Scalar and Vector Projection, asked 11 times in 11 shifts (2020, 2021, 2022, 2024, 2025), most often as “unknown vector from cross and dot conditions”.
- 04
JEE Main has asked 16 of the 64 ideas in this topic; 39 have never been asked, directly or inside another question.
- 05
Mostly asked as single correct (69%); 28% need a numerical answer, 22% are easy and 19% hard.
- 06
The skill tested most is multi-step (56%), then calculation (28%).
Questions a shift, year by year
Out of the 25 Maths questions in a shift. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift.
Raw count: 2017: 0 in 1 shift · 2020: 4 in 12 shifts · 2021: 6 in 24 shifts · 2022: 10 in 24 shifts · 2023: 1 in 12 shifts · 2024: 9 in 18 shifts · 2025: 3 in 8 shifts · 2026: 3 in 9 shifts.
- Up to 2023
- 0.2
- a shift, of 25
- Since 2024
- 0.4
- 0.2
- Usual gap
- 1.0 yrs
- between years asking it
- Shifts with it
- 33/108
- 31% of analysed shifts
How it is asked
Difficulty, format and skill
Across all 36 questions on Dot Product since 2017.
Difficulty
QUESTIONS- Easy8 · 22%
- Medium21 · 58%
- Hard7 · 19%
Format
SHARE- Single correct · 25 Q69%
- Numerical value · 10 Q28%
- Two statements · 1 Q3%
Skill tested
SHARE- Multi-step · 20 Q56%
- Calculation · 10 Q28%
- Application · 5 Q14%
- Conceptual · 1 Q3%
Repeats
New idea, or one asked before?
Each column is a year. Blue questions tested an idea no earlier year had asked; navy ones went back to an idea from an earlier year. 2017 is the first year, so everything in it counts as new. Heights are question counts, and Lumi analysed 1 to 24 shifts a year, so compare the split inside a column rather than heights across years.
- Idea asked for the first time
- Idea asked in an earlier year
Coverage of the topic
JEE Main has asked 16 of the 64 ideas in this topic. 39 have never been asked yet.
- Asked directly16 · 25%
- Touched inside another question9 · 14%
- Never asked39 · 61%
Ideas come from Lumi’s JEE syllabus map. A never-asked idea is not a safe skip: across all of JEE Main, 22% of questions since 2024 tested an idea no earlier year had asked.
Drill down
Chapter, idea, question
Every idea JEE Main tested in this topic, with its eight years. Open one to read the questions.
14 ideas inside
Squares are the 8 years with analysed shifts, 2017 to 2026. A number is the questions that year when there is more than one; the shade is scaled to one shift, so a year with more analysed shifts (1 to 24 a year) does not look darker. Share is of the level above.
Ideas
Every idea inside this topic
16 different ideas were tested; 4 came more than once.
unknown vector from cross and dot conditions
Single correct · 11 shifts · 4 numericalvectors rotation angle then trig value
Single correct · 5 shifts · 1 numericalvalue from ratio of sum and difference magnitudes
Single correct · 4 shifts · 1 numericalparameter set for obtuse angle between vectors
Single correct · 3 shifts · 1 numericalmaximum of combined vector magnitudes
Single correct · 1 shiftunknown vector from dot product conditions
Single correct · 1 shiftunit vector perpendicular to a within plane
Single correct · 1 shiftlength of internal bisector segment in vector triangle
Single correct · 1 shiftvector sum from circumcenter and orthocentre
Single correct · 1 shiftstatement pair on unit vectors
Two statements · 1 shiftmagnitude of cross product from perpendicularity
Single correct · 1 shiftdirection ratios of rhombus diagonal
Numerical value · 1 shift · 1 numericalcomponent of vector along another
Numerical value · 1 shift · 1 numericalprojection of rotated vector
Single correct · 1 shiftcomponents of vector after axes rotation
Single correct · 1 shiftvector magnitude identity from unit vectors
Numerical value · 1 shift · 1 numerical
| Idea | Years asked | Times | Shifts | Format | Numerical |
|---|---|---|---|---|---|
| Scalar and Vector Projectionunknown vector from cross and dot conditions | 11 | 11 | Single correctMulti-step | 4 | |
| Angle Between Vectorsvectors rotation angle then trig value | 6 | 5 | Single correctMulti-step | 1 | |
| Expansion of Sum of Vectors Squaredvalue from ratio of sum and difference magnitudes | 4 | 4 | Single correctCalculation | 1 | |
| Acute and Obtuse Angle Conditionsparameter set for obtuse angle between vectors | 3 | 3 | Single correctApplication | 1 | |
| Parallelogram Law Identitymaximum of combined vector magnitudes | 1 | 1 | Single correctMulti-step | – | |
| Solving Unknown Vector via Dot Productsunknown vector from dot product conditions | 1 | 1 | Single correctCalculation | – | |
| Orthogonal Resolution of a Vectorunit vector perpendicular to a within plane | 1 | 1 | Single correctApplication | – | |
| Angle Bisector Constructionlength of internal bisector segment in vector triangle | 1 | 1 | Single correctMulti-step | – | |
| Orthocenter Position Vector Relationsvector sum from circumcenter and orthocentre | 1 | 1 | Single correctConceptual | – | |
| Lagrange's Identity (Dot Product Form)statement pair on unit vectors | 1 | 1 | Two statementsMulti-step | – | |
| Orthogonality Conditionmagnitude of cross product from perpendicularity | 1 | 1 | Single correctMulti-step | – | |
| Perpendicular Diagonals of a Rhombusdirection ratios of rhombus diagonal | 1 | 1 | Numerical valueMulti-step | 1 | |
| Scalar vs Vector Projection Distinctioncomponent of vector along another | 1 | 1 | Numerical valueCalculation | 1 | |
| Vectors with Equal Inclinationprojection of rotated vector | 1 | 1 | Single correctMulti-step | – | |
| Dot Product Invariance Under Rotationcomponents of vector after axes rotation | 1 | 1 | Single correctApplication | – | |
| Algebraic Propertiesvector magnitude identity from unit vectors | 1 | 1 | Numerical valueCalculation | 1 |
Times and shifts count every analysed shift. Across JEE Main, 78% of questions since 2024 went back to an idea an earlier year had asked; the rest were new. All repeated ideas
Every question
Dot Product questions, year by year
The opening words of each question as it appeared in the official paper, with the idea it tested. Open one for its options and the official answer.
JEE Main 20263 questions in 2 shifts
- 2 Apr, Shift 1Q14If and are two vectors such that and , then the maximum value of…
Idea: Parallelogram Law Identity
New ideaHardSingle correct - 2 Apr, Shift 2Q14Let the vectors and . For some…
Idea: Solving Unknown Vector via Dot Products
New ideaMediumSingle correct - 2 Apr, Shift 2Q16Two adjacent sides of a parallelogram are given by and . If the side…
Idea: Angle Between Vectors
MediumSingle correct
JEE Main 20253 questions in 3 shifts
- 2 Apr, Shift 1Q11If is a nonzero vector such that its projections on the vectors , and…
Idea: Scalar and Vector Projection
Asked the year beforeMediumSingle correct - 7 Apr, Shift 2Q15Let and be the vectors of the same magnitude such that…
Idea: Expansion of Sum of Vectors Squared
Asked the year beforeMediumSingle correct - 8 Apr, Shift 2Q14Let and . Let be a unit vector in the plane of…
Idea: Orthogonal Resolution of a Vector
New ideaMediumSingle correct
JEE Main 20249 questions in 8 shifts
- 4 Apr, Shift 1Q18Let a unit vector which makes an angle of with and an angle of with be…
Idea: Angle Between Vectors
HardSingle correct - 4 Apr, Shift 2Q17Let and . If is…
Idea: Angle Between Vectors
MediumSingle correct - 4 Apr, Shift 2Q18For , let be the angle between the vectors and .…
Idea: Angle Between Vectors
EasySingle correct - 8 Apr, Shift 1Q18The set of all , for which the vectors and…
Idea: Acute and Obtuse Angle Conditions
MediumSingle correct - 8 Apr, Shift 2Q18Let , and…
Idea: Scalar and Vector Projection
MediumSingle correct - 1 Feb, Shift 2Q17Consider a where , and . If the angle bisector of meets the line at ,…
Idea: Scalar and Vector Projection
MediumSingle correct - 27 Jan, Shift 1Q28The least positive integral value of , for which the angle between the vectors and…
Idea: Acute and Obtuse Angle Conditions
EasyNumerical value - 29 Jan, Shift 1Q18Let O be the origin and the position vectors of A and B be and respectively. If…
Idea: Angle Bisector Construction
New ideaMediumSingle correct - 30 Jan, Shift 2Q18Let and be two vectors such that and . Then…
Idea: Expansion of Sum of Vectors Squared
EasySingle correct
JEE Main 20231 question in 1 shift
- 10 Apr, Shift 2Q17If the points P and Q are respectively the circumcenter and the orthocentre of a , then…
Idea: Orthocenter Position Vector Relations
New ideaMediumSingle correct
JEE Main 202210 questions in 9 shifts
- 25 Jul, Shift 2Q17Let and let be a vector such that and…
Idea: Scalar and Vector Projection
Asked the year beforeMediumSingle correct - 26 Jul, Shift 2Q51If m and m. The magnitude of…
Idea: Scalar vs Vector Projection Distinction
New ideaEasyNumerical value - 28 Jul, Shift 1Q6Let a vector has magnitude 9. Let a vector be such that for every , the…
Idea: Orthogonality Condition
New ideaMediumSingle correct - 28 Jul, Shift 1Q22Let and be the vertices of the rhombus PRQS. If the direction…
Idea: Perpendicular Diagonals of a Rhombus
New ideaMediumNumerical value - 28 Jul, Shift 2Q77Let S be the set of all for which the angle between the vectors and…
Idea: Acute and Obtuse Angle Conditions
New ideaMediumSingle correct - 30 Jul, Shift 2Q88Let be a parallelogram, be the origin, and . If and ,…
Idea: Scalar and Vector Projection
Asked the year beforeHardNumerical value - 24 Jun, Shift 2Q16Let and be two unit vectors such that . If…
Idea: Lagrange's Identity (Dot Product Form)
New ideaHardTwo statements - 25 Jun, Shift 1Q14Let , be a vector which makes equal angles with the coordinate axes OX, OY and…
Idea: Vectors with Equal Inclination
New ideaHardSingle correct - 26 Jun, Shift 2Q16Let , and be…
Idea: Scalar and Vector Projection
Asked the year beforeMediumSingle correct - 29 Jun, Shift 1Q5Let , and…
Idea: Scalar and Vector Projection
Asked the year beforeMediumSingle correct
JEE Main 20216 questions in 6 shifts
- 26 Aug, Shift 2Q87If the projection of the vector on the sum of the two vectors and…
Idea: Scalar and Vector Projection
Asked the year beforeEasyNumerical value - 31 Aug, Shift 1Q78Let and be two vectors such that…
Idea: Expansion of Sum of Vectors Squared
Asked the year beforeMediumSingle correct - 25 Jul, Shift 2Q88If is perpendicular to and is…
Idea: Angle Between Vectors
Asked the year beforeMediumNumerical value - 17 Mar, Shift 2Q89Let be a vector in the plane containing vectors and…
Idea: Scalar and Vector Projection
Asked the year beforeHardNumerical value - 18 Mar, Shift 1Q80A vector has components 3p and 1 with respect to a rectangular cartesian system. This system is rotated through a certain angle…
Idea: Dot Product Invariance Under Rotation
New ideaMediumSingle correct - 18 Mar, Shift 2Q66In a triangle ABC, if , , ,…
Idea: Scalar and Vector Projection
Asked the year beforeMediumSingle correct
JEE Main 20204 questions in 4 shifts
- 9 Jan, Shift 1Q75The projection of the line segment joining the points (1, , 3) and (2, , 11) on the line joining the points (, 2, 3) and (3,…
Idea: Scalar and Vector Projection
New ideaEasyNumerical value - 2 Sep, Shift 1Q75Let , and be three unit vectors such that . Then…
Idea: Algebraic Properties
New ideaEasyNumerical value - 3 Sep, Shift 2Q69Let a, b, be such that . If…
Idea: Angle Between Vectors
New ideaHardSingle correct - 6 Sep, Shift 2Q74If and be two non-zero vectors such that and is perpendicular…
Idea: Expansion of Sum of Vectors Squared
New ideaEasyNumerical value
Questions from the official JEE Main Paper 1 shifts published by NTA (CBSE for 2017). Questions NTA dropped are left out. Topic and idea tags, counts and notes are Lumi’s.