JEE Main 2024 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 5 April 2024, Shift 1, Maths Q18

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

A(1,-1,2)

B(5,7,-6)

C(3,4,-10)

and

D(-1,-4,-2)

are the vertices of a quadrilateral ABCD, then its area is :

(1) $12\sqrt{29}$ Official answer
(2) $24\sqrt{29}$
(3) $48\sqrt{7}$
(4) $24\sqrt{7}$

Official answer

Option 1

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

6 Apr 2024, Shift 1 · Q19If $A(3,1,-1)$ , $B\left(\frac{5}{3},\frac{7}{3},\frac{1}{3}\right)$ , $C(2,2,1)$ and $D\left(\frac{10}{3},\frac{2}{3},\frac{-1}{3}\right)$ …MediumSingle correct
9 Apr 2024, Shift 1 · Q17Let $\overrightarrow{OA}=2\vec{a}$ , $\overrightarrow{OB}=6\vec{a}+5\vec{b}$ and $\overrightarrow{OC}=3\vec{b}$ , where O is the origin. If…MediumSingle correct
9 Apr 2024, Shift 2 · Q18Let $\vec{a}=2\hat{i}+\alpha\hat{j}+\hat{k},\ \vec{b}=-\hat{i}+\hat{k},\ \vec{c}=\beta\hat{j}-\hat{k}$ , where $\alpha$ and $\beta$ are…MediumSingle correct
30 Jan 2024, Shift 1 · Q17Let $A(2,3,5)$ and $C(-3,4,-2)$ be opposite vertices of a parallelogram $ABCD$ . If the diagonal…MediumSingle correct
8 Apr 2023, Shift 2 · Q15The area of the quadrilateral $ABCD$ with vertices $A(2, 1, 1)$ , $B(1, 2, 5)$ , $C(-2, -3, 5)$ and $D(1, -6, -7)$ is equal toMediumSingle correct
27 Jun 2022, Shift 2 · Q15Let $\vec{a}$ and $\vec{b}$ be the vectors along the diagonals of a parallelogram having area $2\sqrt{2}$ . Let the angle between $\vec{a}$ …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.