JEE Main · Maths · Vector Algebra
Triple Products: JEE Main previous year questions
30 questions in the 108 JEE Main shifts Lumi analysed, in 5 of 8 years. Pattern: Asked most years. 2 came in 2024–26. Here is how it is asked and which ideas come back.
- Questions
- 30
- in 28 of 108 shifts
- Years asked
- 5/8
- last asked 2024
- Weighted estimate
- 0.1
- model; history: 0.2 a shift on average, typically 0.0–0.4
Key findings
- 01
Asked in 5 of 8 years with analysed shifts and in 28 of 108 shifts: 30 questions, #113 of 196 topics. Last asked in 2024.
- 02
37% of its questions since 2020 tested an idea no earlier year had asked; 16 repeated an idea from the year before.
- 03
The most repeated idea is Solving for Unknown in Coplanarity, asked 7 times in 7 shifts (2020, 2021, 2022, 2023), most often as “coplanarity of three vectors with parameters”.
- 04
JEE Main has asked 10 of the 64 ideas in this topic; 50 have never been asked, directly or inside another question.
- 05
Mostly asked as single correct (80%); 20% need a numerical answer, 3% are easy and 13% hard. It went down from 0.3 to 0.0 questions a shift since 2024.
- 06
The skill tested most is multi-step (60%), then calculation (27%).
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: 5 in 12 shifts · 2021: 10 in 24 shifts · 2022: 6 in 24 shifts · 2023: 7 in 12 shifts · 2024: 2 in 18 shifts · 2025: 0 in 8 shifts · 2026: 0 in 9 shifts.
- Up to 2023
- 0.3
- a shift, of 25
- Since 2024
- 0.0
- -0.3
- Usual gap
- 1.0 yrs
- between years asking it
- Shifts with it
- 28/108
- 26% of analysed shifts
How it is asked
Difficulty, format and skill
Across all 30 questions on Triple Products since 2017.
Difficulty
QUESTIONS- Easy1 · 3%
- Medium25 · 83%
- Hard4 · 13%
Format
SHARE- Single correct · 24 Q80%
- Numerical value · 6 Q20%
Skill tested
SHARE- Multi-step · 18 Q60%
- Calculation · 8 Q27%
- Application · 3 Q10%
- 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 10 of the 64 ideas in this topic. 50 have never been asked yet.
- Asked directly10 · 16%
- Touched inside another question4 · 6%
- Never asked50 · 78%
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.
10 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
10 different ideas were tested; 6 came more than once.
coplanarity of three vectors with parameters
Single correct · 7 shifts · 2 numericalparameter values for coplanar points
Single correct · 5 shiftsunknown scalar from vector triple product equation
Single correct · 4 shiftsunknown vector from cross and dot conditions
Numerical value · 4 shifts · 2 numericalnested vector triple product then projection
Single correct · 3 shiftsangle between edges from parallelepiped volume
Single correct · 3 shiftscoplanarity of two vector triples
Single correct · 1 shiftmagnitude of vector from coplanar and dot conditions
Numerical value · 1 shift · 1 numericalsum of scalar triple products with coplanar and perpendicular conditions
Single correct · 1 shiftvector triple product magnitudes sum
Numerical value · 1 shift · 1 numerical
| Idea | Years asked | Times | Shifts | Format | Numerical |
|---|---|---|---|---|---|
| Solving for Unknown in Coplanaritycoplanarity of three vectors with parameters | 7 | 7 | Single correctMulti-step | 2 | |
| Coplanarity of Four Pointsparameter values for coplanar points | 5 | 5 | Single correctCalculation | – | |
| VTP BAC-CAB Expansionunknown scalar from vector triple product equation | 4 | 4 | Single correctMulti-step | – | |
| STP Definition and Determinantunknown vector from cross and dot conditions | 4 | 4 | Numerical valueMulti-step | 2 | |
| VTP with Repeated Vectorsnested vector triple product then projection | 3 | 3 | Single correctApplication | – | |
| STP Geometric Interpretationangle between edges from parallelepiped volume | 3 | 3 | Single correctApplication | – | |
| Parametric Coplanarity via STPcoplanarity of two vector triples | 1 | 1 | Single correctMulti-step | – | |
| Constructing Orthogonal Coplanar Vectorsmagnitude of vector from coplanar and dot conditions | 1 | 1 | Numerical valueMulti-step | 1 | |
| STP Algebraic Propertiessum of scalar triple products with coplanar and perpendicular conditions | 1 | 1 | Single correctMulti-step | – | |
| Perpendicular Vector Component via VTPvector triple product magnitudes sum | 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
Triple Products 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 20242 questions in 2 shifts
- 6 Apr, Shift 2Q18Let , . Then…
Idea: VTP with Repeated Vectors
MediumSingle correct - 1 Feb, Shift 1Q19Let , and…
Idea: VTP with Repeated Vectors
MediumSingle correct
JEE Main 20237 questions in 6 shifts
- 6 Apr, Shift 1Q15Let the position vectors of the points A, B, C and D be , ,…
Idea: Coplanarity of Four Points
Asked the year beforeMediumSingle correct - 6 Apr, Shift 2Q17The sum of all values of , for which the points whose position vectors are ,…
Idea: Coplanarity of Four Points
Asked the year beforeMediumSingle correct - 6 Apr, Shift 2Q18Let the vectors represent three coterminous edges of a parallelopiped of volume V. Then the volume of the…
Idea: STP Geometric Interpretation
MediumSingle correct - 8 Apr, Shift 2Q16Let the vectors , and…
Idea: Parametric Coplanarity via STP
New ideaHardSingle correct - 11 Apr, Shift 2Q17If four distinct points with position vectors and are coplanar, then …
Idea: Coplanarity of Four Points
Asked the year beforeMediumSingle correct - 12 Apr, Shift 1Q16Let be three distinct real numbers, none equal to one. If the vectors , and…
Idea: Solving for Unknown in Coplanarity
Asked the year beforeMediumSingle correct - 15 Apr, Shift 1Q16Let be the set of all for which the vectors , and…
Idea: Solving for Unknown in Coplanarity
Asked the year beforeMediumSingle correct
JEE Main 20226 questions in 6 shifts
- 27 Jul, Shift 1Q13Let and . If…
Idea: VTP BAC-CAB Expansion
Asked the year beforeMediumSingle correct - 29 Jul, Shift 1Q10Let and . Let be a vector satisfying…
Idea: VTP BAC-CAB Expansion
Asked the year beforeMediumSingle correct - 29 Jul, Shift 2Q15If , , and are coplanar, then the product of all possible values of is :
Idea: Coplanarity of Four Points
Asked the year beforeMediumSingle correct - 26 Jun, Shift 1Q16If , and , then the value of…
Idea: VTP BAC-CAB Expansion
Asked the year beforeMediumSingle correct - 28 Jun, Shift 1Q24If , and are coplanar…
Idea: Solving for Unknown in Coplanarity
Asked the year beforeMediumNumerical value - 30 Jun, Shift 1Q17Let a vector be coplanar with the vectors and .…
Idea: Solving for Unknown in Coplanarity
Asked the year beforeHardSingle correct
JEE Main 202110 questions in 9 shifts
- 31 Aug, Shift 2Q75Let be three vectors mutually perpendicular to each other and have same magnitude. If a vector …
Idea: VTP BAC-CAB Expansion
New ideaHardSingle correct - 24 Feb, Shift 1Q89Let three vectors and be such that is coplanar with and ,…
Idea: Constructing Orthogonal Coplanar Vectors
New ideaMediumNumerical value - 26 Feb, Shift 1Q61If and are perpendicular, then is equal to :
Idea: VTP with Repeated Vectors
New ideaEasySingle correct - 26 Feb, Shift 1Q62If , , and are coplanar, then the sum of all possible values of is :
Idea: Coplanarity of Four Points
New ideaMediumSingle correct - 22 Jul, Shift 2Q80Let a vector be coplanar with vectors and…
Idea: STP Algebraic Properties
New ideaHardSingle correct - 25 Jul, Shift 1Q71Let the vectors , and…
Idea: Solving for Unknown in Coplanarity
Asked the year beforeMediumSingle correct - 25 Jul, Shift 2Q80Let a, b and c be distinct positive numbers. If the vectors , and…
Idea: Solving for Unknown in Coplanarity
Asked the year beforeMediumSingle correct - 16 Mar, Shift 2Q84Let be a vector perpendicular to the vectors and . If…
Idea: STP Definition and Determinant
Asked the year beforeMediumNumerical value - 17 Mar, Shift 1Q90If , and …
Idea: STP Definition and Determinant
Asked the year beforeMediumNumerical value - 17 Mar, Shift 2Q63Let O be the origin. Let and ,…
Idea: STP Definition and Determinant
Asked the year beforeMediumSingle correct
JEE Main 20205 questions in 5 shifts
- 8 Jan, Shift 1Q66Let the volume of a parallelopiped whose coterminous edges are given by ,…
Idea: STP Geometric Interpretation
New ideaMediumSingle correct - 9 Jan, Shift 1Q73If the vectors, , and…
Idea: Solving for Unknown in Coplanarity
New ideaMediumNumerical value - 4 Sep, Shift 1Q67Let be the point of local maxima of , where…
Idea: STP Definition and Determinant
New ideaMediumSingle correct - 4 Sep, Shift 2Q75If , then the value of…
Idea: Perpendicular Vector Component via VTP
New ideaMediumNumerical value - 5 Sep, Shift 1Q67If the volume of a parallelopiped, whose coterminus edges are given by the vectors ,…
Idea: STP Geometric Interpretation
New ideaMediumSingle correct
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.