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Saturday, 31 October

JEE Main 2024 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 9 April 2024, Shift 2, Maths Q18

Question 18 of 90 in this shift, Maths question 18 of 30, Section A.

Let 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 integers and αβ=−6\alpha\beta=-6. Let the values of the ordered pair (α,β)(\alpha, \beta), for which the area of the parallelogram of diagonals a⃗+b⃗\vec{a}+\vec{b} and b⃗+c⃗\vec{b}+\vec{c} is 212\frac{\sqrt{21}}{2}, be (α1,β1)(\alpha_1,\beta_1) and (α2,β2)(\alpha_2,\beta_2). Then α12+β12−α2β2\alpha_1^2+\beta_1^2-\alpha_2\beta_2 is equal to
  1. (1)1717
  2. (2)1919Official answer
  3. (3)2121
  4. (4)2424

Official answer

Option 2

NTA final key.

Chapter
Vector Algebra
Topic
Cross Product
Idea tested
Area of Quadrilateral via Diagonals

Same idea in other shifts

Asked 7× in all
  1. 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
  2. 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
  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. 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
  5. 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
  6. 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

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.