JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 28 June 2022, Shift 2, Maths Q14

Question 14 of 90 in this shift, Maths question 14 of 30, Section A.

Let

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

and

\vec{b}=-2\hat{i}+\alpha\hat{j}+\hat{k}

, where

\alpha \in \mathbf{R}

. If the area of the parallelogram whose adjacent sides are represented by the vectors

\vec{a}

and

\vec{b}

\sqrt{15(\alpha^2+4)}

, then the value of

2|\vec{a}|^2+(\vec{a}\cdot\vec{b})|\vec{b}|^2

is equal to :

(1)10
(2)7
(3)9
(4)14Official answer

Official answer

Option 4

NTA final key.

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

Same idea in other shifts

Asked 7× 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
4 Apr 2024, Shift 1 · Q30Let ABC be a triangle of area $15\sqrt{2}$ and the vectors $\overrightarrow{AB}=\hat{i}+2\hat{j}-7\hat{k}$ ,…HardNumerical value
9 Apr 2024, Shift 1 · Q18Let three vectors $\vec{a}=\alpha\hat{i}+4\hat{j}+2\hat{k}$ , $\vec{b}=5\hat{i}+3\hat{j}+4\hat{k}$ , $\vec{c}=x\hat{i}+y\hat{j}+z\hat{k}$ …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
25 Feb 2021, Shift 2 · Q90Let $\vec{a} = \hat{i} + \alpha\hat{j} + 3\hat{k}$ and $\vec{b} = 3\hat{i} - \alpha\hat{j} + \hat{k}$ . If the area of the parallelogram…EasyNumerical value

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.