JEE Main 2021 · MathsNumerical answerNumerical valueEasyCalculation

JEE Main 25 February 2021, Shift 2, Maths Q90

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

Let

\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 whose adjacent sides are represented by the vectors

\vec{a}

and

\vec{b}

8\sqrt{3}

square units, then

\vec{a} \cdot \vec{b}

is equal to ________.

Official answer

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
28 Jun 2022, Shift 2 · Q14Let $\vec{a}=\alpha\hat{i}+2\hat{j}-\hat{k}$ and $\vec{b}=-2\hat{i}+\alpha\hat{j}+\hat{k}$ , where $\alpha \in \mathbf{R}$ . If the area of…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 108 of the 174 JEE Main shifts held from 2017 to 2026.