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Saturday, 31 October

JEE Main · Maths · Vector Algebra

Area of Triangles and Parallelograms

JEE Main asked Area of Triangles and Parallelograms 7 times in 7 of the 108 shifts Lumi analysed, in 2021, 2022, 2023, 2024, 2025 and 2026. It belongs to Cross Product, in Vector Algebra (Maths). The longest wait between two years asking it was 1 year. In 2024 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
7
in 7 shifts
Years
6 of 8
First asked
2021
last in 2026
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2021, 2022, 2023, 2024, 2025 and 2026. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.10.20’170’200.03’210.04’220.07’230.09’240.13’250.11’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 1 in 24 shifts · 2022: 1 in 24 shifts · 2023: 1 in 12 shifts · 2024: 2 in 18 shifts · 2025: 1 in 8 shifts · 2026: 1 in 9 shifts.

Shift by shift

Each square is one analysed shift, in date order. Open a filled one for that paper.

  • 20261 of 9
  • 20251 of 8
  • 20242 of 18
  • 20231 of 12
  • 20221 of 24
  • 20211 of 24
  • 20200 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Single correct is the usual form. Skill tested: multi-step.

  • Area of triangle from vector combinations
  • Area of face of right-corner tetrahedron

Difficulty

Easy 2Medium 4Hard 1

2 of the 7 questions had a numerical answer.

Every question

All 7 questions

From the official JEE Main shift papers, newest first. Open one for the full question, the options and the official answer.

  1. 6 Apr 2026, Shift 2 · Q15Let a⃗=2i^+3j^+3k^\vec{a}=2\hat{i}+3\hat{j}+3\hat{k} and b⃗=6i^+3j^+3k^\vec{b}=6\hat{i}+3\hat{j}+3\hat{k}. Then the square of the area of the triangle with…EasySingle correct
  2. 2 Apr 2025, Shift 1 · Q5Let ABCD be a tetrahedron such that the edges AB, AC and AD are mutually perpendicular. Let the areas of the triangles ABC, ACD and ADB be…MediumSingle correct
  3. 9 Apr 2024, Shift 1 · Q18Let three vectors a⃗=αi^+4j^+2k^\vec{a}=\alpha\hat{i}+4\hat{j}+2\hat{k}, b⃗=5i^+3j^+4k^\vec{b}=5\hat{i}+3\hat{j}+4\hat{k}, c⃗=xi^+yj^+zk^\vec{c}=x\hat{i}+y\hat{j}+z\hat{k}…MediumSingle correct
  4. 4 Apr 2024, Shift 1 · Q30Let ABC be a triangle of area 15215\sqrt{2} and the vectors AB→=i^+2j^−7k^\overrightarrow{AB}=\hat{i}+2\hat{j}-7\hat{k},…HardNumerical value
  5. 13 Apr 2023, Shift 2 · Q18Let for a triangle ABC, AB→=−2i^+j^+3k^\overrightarrow{AB}=-2\hat{i}+\hat{j}+3\hat{k} CB→=αi^+βj^+γk^\overrightarrow{CB}=\alpha\hat{i}+\beta\hat{j}+\gamma\hat{k}…MediumSingle correct
  6. 28 Jun 2022, Shift 2 · Q14Let a⃗=αi^+2j^−k^\vec{a}=\alpha\hat{i}+2\hat{j}-\hat{k} and b⃗=−2i^+αj^+k^\vec{b}=-2\hat{i}+\alpha\hat{j}+\hat{k}, where α∈R\alpha \in \mathbf{R}. If the area of…MediumSingle correct
  7. 25 Feb 2021, Shift 2 · Q90Let a⃗=i^+αj^+3k^\vec{a} = \hat{i} + \alpha\hat{j} + 3\hat{k} and b⃗=3i^−αj^+k^\vec{b} = 3\hat{i} - \alpha\hat{j} + \hat{k}. If the area of the parallelogram…EasyNumerical value

Shifts: 25 Feb 2021, Shift 2, 28 Jun 2022, Shift 2, 13 Apr 2023, Shift 2, 4 Apr 2024, Shift 1, 9 Apr 2024, Shift 1, 2 Apr 2025, Shift 1, 6 Apr 2026, Shift 2.

Same topic

Other ideas in Cross Product

Cross Product has 13 ideas JEE Main has asked; 9 of them came up in more than one question.

Topic analysisChapter analysisStudy this chapterAll repeated ideas