JEE Main 2024 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 30 January 2024, Shift 1, Maths Q17

Question 17 of 90 in this shift, Maths question 17 of 30, Section A.

Let

A(2,3,5)

and

C(-3,4,-2)

be opposite vertices of a parallelogram

ABCD

. If the diagonal

\overrightarrow{BD}=\hat{i}+2\hat{j}+3\hat{k}

, then the area of the parallelogram is equal to :

(1) $\frac{1}{2}\sqrt{474}$ Official answer
(2) $\frac{1}{2}\sqrt{306}$
(3) $\frac{1}{2}\sqrt{410}$
(4) $\frac{1}{2}\sqrt{586}$

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

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
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.