JEE Main 2023 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 8 April 2023, Shift 2, Maths Q15

Question 15 of 90 in this shift, Maths question 15 of 30, Section A.

The 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 to

(1)48
(2) $8\sqrt{38}$ Official answer
(3) $9\sqrt{38}$
(4)54

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

5 Apr 2024, Shift 1 · Q18If $A(1,-1,2)$ , $B(5,7,-6)$ , $C(3,4,-10)$ and $D(-1,-4,-2)$ are the vertices of a quadrilateral ABCD, then its area is :MediumSingle correct
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
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.