JEE Main 2022 · MathsNumerical answerNumerical valueMediumCalculation

JEE Main 25 June 2022, Shift 1, Maths Q23

Question 23 of 90 in this shift, Maths question 23 of 30, Section B.

Let

\theta

be the angle between the vectors

\vec{a}

and

\vec{b}

, where

|\vec{a}|=4

|\vec{b}|=3

and

\theta\in\left(\frac{\pi}{4},\frac{\pi}{3}\right)

. Then

\left|\left(\vec{a}-\vec{b}\right)\times\left(\vec{a}+\vec{b}\right)\right|^2+4\left(\vec{a}\cdot\vec{b}\right)^2

is equal to __________.

Official answer

576

NTA final key.

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

Same idea in other shifts

Asked 8× in all

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31 Jan 2024, Shift 1 · Q30Let $\vec{a}$ and $\vec{b}$ be two vectors such that $|\vec{a}|=1,\ |\vec{b}|=4$ , and $\vec{a}\cdot\vec{b}=2$ . If…MediumNumerical value
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
29 Jul 2022, Shift 2 · Q18Let $\vec{a},\vec{b},\vec{c}$ be three coplanar concurrent vectors such that angles between any two of them is same. If the product of…HardSingle correct
29 Jul 2022, Shift 2 · Q29Let $\vec{a}$ and $\vec{b}$ be two vectors such that $|\vec{a}+\vec{b}|^2=|\vec{a}|^2+2|\vec{b}|^2$ , $\vec{a}\cdot\vec{b}=3$ and…MediumNumerical value
25 Jul 2021, Shift 2 · Q78If $|\vec{a}|=2$ , $|\vec{b}|=5$ and $|\vec{a}\times\vec{b}|=8$ , then $|\vec{a}\cdot\vec{b}|$ is equal to :EasySingle correct
2 Sep 2020, Shift 2 · Q73Let the position vectors of points 'A' and 'B' be $\hat{i}+\hat{j}+\hat{k}$ and $2\hat{i}+\hat{j}+3\hat{k}$ , respectively. A point 'P'…MediumNumerical 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.