JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 27 July 2022, Shift 2, Maths Q30

Question 30 of 90 in this shift, Maths question 30 of 30, Section B. NTA dropped this question from the final key; it is left out of every count on this site.

Let

\vec{a}, \vec{b}, \vec{c}

be three non-coplanar vectors such that

\vec{a} \times \vec{b} = 4\vec{c}

\vec{b} \times \vec{c} = 9\vec{a}

and

\vec{c} \times \vec{a} = \alpha\vec{b}

\alpha > 0

. If

|\vec{a}| + |\vec{b}| + |\vec{c}| = \frac{1}{36}

, then

\alpha

is equal to __________.

Official answer

Dropped by NTA (marks given to all)

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.