JEE Main 2020 · MathsNumerical answerNumerical valueMediumCalculation

JEE Main 2 September 2020, Shift 2, Maths Q73

Question 73 of 75 in this shift, Maths question 23 of 25.

Let 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' divides the line segment AB internally in the ratio

\lambda:1

(

\lambda>0

). If O is the origin and

\overrightarrow{OB}\cdot\overrightarrow{OP}-3\left|\overrightarrow{OA}\times\overrightarrow{OP}\right|^2=6

, then

\lambda

is equal to ________.

Official answer

0.80

NTA final key (Sep 2020).

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

Same idea in other shifts

Asked 8× 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
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 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

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.