JEE Main 2021 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 27 August 2021, Shift 1, Maths Q89

Question 89 of 90 in this shift, Maths question 29 of 30, Section B.

Let

\vec{a}=\hat{i}+5\hat{j}+\alpha\hat{k}

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

and

\vec{c}=-\hat{i}+2\hat{j}-3\hat{k}

be three vectors such that,

|\vec{b}\times\vec{c}|=5\sqrt{3}

and

\vec{a}

is perpendicular to

\vec{b}

. Then the greatest amongst the values of

|\vec{a}|^2

is ___________.

Official answer

NTA final key.

Chapter: Vector Algebra
Topic: Cross Product
Idea tested: Magnitude and Sine Formula

Same idea in other shifts

Asked 13× in all

4 Apr 2026, Shift 2 · Q15Let $\hat u$ and $\hat v$ be unit vectors inclined at an acute angle such that $|\hat u\times\hat v|=\frac{\sqrt3}{2}$ . If…HardSingle correct
5 Apr 2024, Shift 2 · Q19Consider three vectors $\vec{a}, \vec{b}, \vec{c}$ . Let $|\vec{a}| = 2$ , $|\vec{b}| = 3$ and $\vec{a} = \vec{b} \times \vec{c}$ . If…HardSingle correct
6 Apr 2024, Shift 2 · Q19Let $\vec{a}=6\hat{i}+\hat{j}-\hat{k}$ and $\vec{b}=\hat{i}+\hat{j}$ . If $\vec{c}$ is a vector such that $|\vec{c}|\ge 6$ ,…HardSingle correct
30 Jan 2024, Shift 1 · Q18Let $\vec{a}=a_1\hat{i}+a_2\hat{j}+a_3\hat{k}$ and $\vec{b}=b_1\hat{i}+b_2\hat{j}+b_3\hat{k}$ be two vectors such that $|\vec{a}|=1$ ,…HardSingle correct
11 Apr 2023, Shift 1 · Q11Let $\vec{a}$ be a non-zero vector parallel to the line of intersection of the two planes described by $\hat{i}+\hat{j},\ \hat{i}+\hat{k}$ …HardSingle correct
11 Apr 2023, Shift 2 · Q29Let $\vec{a} = \hat{i} + 2\hat{j} + 3\hat{k}$ and $\vec{b} = \hat{i} + \hat{j} - \hat{k}$ . If $\vec{c}$ is a vector such that…HardNumerical value
25 Jul 2022, Shift 1 · Q15Let $ABC$ be a triangle such that $\overrightarrow{BC}=\vec a$ , $\overrightarrow{CA}=\vec b$ , $\overrightarrow{AB}=\vec c$ ,…HardTwo statements
26 Jul 2022, Shift 1 · Q15Let $\overrightarrow{\mathrm{a}} = \alpha \hat{i} + \hat{j} - \hat{k}$ and…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.