JEE Main 2022 · MathsNumerical answerNumerical valueMediumCalculation

JEE Main 29 July 2022, Shift 2, Maths Q29

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

Let

\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

|\vec{a}\times\vec{b}|^2=75

. Then

|\vec{a}|^2

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 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
25 Jun 2022, Shift 1 · Q23Let $\theta$ be the angle between the vectors $\vec{a}$ and $\vec{b}$ , where $|\vec{a}|=4$ , $|\vec{b}|=3$ 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.