JEE Main 2024 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 9 April 2024, Shift 1, Maths Q18

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

Let three vectors

\vec{a}=\alpha\hat{i}+4\hat{j}+2\hat{k}

\vec{b}=5\hat{i}+3\hat{j}+4\hat{k}

\vec{c}=x\hat{i}+y\hat{j}+z\hat{k}

form a triangle such that

\vec{c}=\vec{a}-\vec{b}

and the area of the triangle is

5\sqrt{6}

. If

\alpha

is a positive real number, then

|\vec{c}|^2

is equal to :

(1) $10$
(2) $12$
(3) $14$ Official answer
(4) $16$

Official answer

Option 3

NTA final key.

Chapter: Vector Algebra
Topic: Cross Product
Idea tested: Area of Triangles and Parallelograms

Same idea in other shifts

Asked 4× in all

6 Apr 2026, Shift 2 · Q15Let $\vec{a}=2\hat{i}+3\hat{j}+3\hat{k}$ and $\vec{b}=6\hat{i}+3\hat{j}+3\hat{k}$ . Then the square of the area of the triangle with…EasySingle correct
2 Apr 2025, Shift 1 · Q5Let ABCD be a tetrahedron such that the edges AB, AC and AD are mutually perpendicular. Let the areas of the triangles ABC, ACD and ADB be…MediumSingle correct
13 Apr 2023, Shift 2 · Q18Let for a triangle ABC, $\overrightarrow{AB}=-2\hat{i}+\hat{j}+3\hat{k}$ $\overrightarrow{CB}=\alpha\hat{i}+\beta\hat{j}+\gamma\hat{k}$ …MediumSingle 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 42 of the 174 JEE Main shifts held from 2017 to 2026.