JEE Main 2024 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 31 January 2024, Shift 1, Maths Q30

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

Let

\vec{a}

and

\vec{b}

be two vectors such that

|\vec{a}|=1,\ |\vec{b}|=4

, and

\vec{a}\cdot\vec{b}=2

. If

\vec{c}=\left(2\vec{a}\times\vec{b}\right)-3\vec{b}

and the angle between

\vec{b}

and

\vec{c}

\alpha

, then

192\sin^2\alpha

is equal to ______

Official answer

NTA final key.

Chapter: Vector Algebra
Topic: Cross Product
Idea tested: Lagrange's Identity

Same idea in other shifts

Asked 3× in all

30 Jan 2024, Shift 2 · Q19Let $\vec{a} = \hat{i} + \alpha\hat{j} + \beta\hat{k}$ , $\alpha, \beta \in \mathbb{R}$ . Let a vector $\vec{b}$ be such that the angle…MediumSingle correct
6 Apr 2023, Shift 1 · Q16Let $\vec a=2\hat i+3\hat j+4\hat k$ , $\vec b=\hat i-2\hat j-2\hat k$ and $\vec c=-\hat i+4\hat j+3\hat k$ . If $\vec d$ is a vector…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.