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Saturday, 31 October

JEE Main · Maths · Vector Algebra

Area of Quadrilateral via Diagonals

JEE Main asked Area of Quadrilateral via Diagonals 7 times in 7 of the 108 shifts Lumi analysed, in 2022, 2023 and 2024. 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
3 of 8
First asked
2022
last in 2024
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

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

00.150.30’170’200’210.04’220.07’230.23’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 0 in 24 shifts · 2022: 1 in 24 shifts · 2023: 1 in 12 shifts · 2024: 5 in 18 shifts · 2025: 0 in 8 shifts · 2026: 0 in 9 shifts.

Shift by shift

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

  • 20260 of 9
  • 20250 of 8
  • 20245 of 18
  • 20231 of 12
  • 20221 of 24
  • 20210 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: calculation.

  • Area of quadrilateral from vertices
  • Unknown parameters from parallelogram area

Difficulty

Easy 0Medium 6Hard 1

Every question was multiple choice.

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. 30 Jan 2024, Shift 1 · Q17Let A(2,3,5)A(2,3,5) and C(−3,4,−2)C(-3,4,-2) be opposite vertices of a parallelogram ABCDABCD. If the diagonal…MediumSingle correct
  2. 9 Apr 2024, Shift 2 · Q18Let a⃗=2i^+αj^+k^, b⃗=−i^+k^, c⃗=βj^−k^\vec{a}=2\hat{i}+\alpha\hat{j}+\hat{k},\ \vec{b}=-\hat{i}+\hat{k},\ \vec{c}=\beta\hat{j}-\hat{k}, where α\alpha and β\beta are…MediumSingle correct
  3. 9 Apr 2024, Shift 1 · Q17Let OA→=2a⃗\overrightarrow{OA}=2\vec{a}, OB→=6a⃗+5b⃗\overrightarrow{OB}=6\vec{a}+5\vec{b} and OC→=3b⃗\overrightarrow{OC}=3\vec{b}, where O is the origin. If…MediumSingle correct
  4. 6 Apr 2024, Shift 1 · Q19If A(3,1,−1)A(3,1,-1), B(53,73,13)B\left(\frac{5}{3},\frac{7}{3},\frac{1}{3}\right), C(2,2,1)C(2,2,1) and D(103,23,−13)D\left(\frac{10}{3},\frac{2}{3},\frac{-1}{3}\right)…MediumSingle correct
  5. 5 Apr 2024, Shift 1 · Q18If A(1,−1,2)A(1,-1,2), B(5,7,−6)B(5,7,-6), C(3,4,−10)C(3,4,-10) and D(−1,−4,−2)D(-1,-4,-2) are the vertices of a quadrilateral ABCD, then its area is :MediumSingle correct
  6. 8 Apr 2023, Shift 2 · Q15The area of the quadrilateral ABCDABCD with vertices A(2,1,1)A(2, 1, 1), B(1,2,5)B(1, 2, 5), C(−2,−3,5)C(-2, -3, 5) and D(1,−6,−7)D(1, -6, -7) is equal toMediumSingle correct
  7. 27 Jun 2022, Shift 2 · Q15Let a⃗\vec{a} and b⃗\vec{b} be the vectors along the diagonals of a parallelogram having area 222\sqrt{2}. Let the angle between a⃗\vec{a}…HardSingle correct

Shifts: 27 Jun 2022, Shift 2, 8 Apr 2023, Shift 2, 30 Jan 2024, Shift 1, 5 Apr 2024, Shift 1, 6 Apr 2024, Shift 1, 9 Apr 2024, Shift 2, 9 Apr 2024, Shift 1.

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