JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 27 August 2021, Shift 2, Maths Q76

Question 76 of 90 in this shift, Maths question 16 of 30, Section A.

The angle between the straight lines, whose direction cosines are given by the equations

2l + 2m - n = 0

and

mn + nl + lm = 0

, is :

(1) $\frac{\pi}{3}$
(2) $\cos^{-1}\left(\frac{8}{9}\right)$
(3) $\frac{\pi}{2}$ Official answer
(4) $\pi - \cos^{-1}\left(\frac{4}{9}\right)$

Official answer

Option 3

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Angle Between Lines
Idea tested: Angle via Direction Cosines

Same topic in other shifts

All Angle Between Lines questions

6 Apr 2026, Shift 1 · Q16Let a line L be perpendicular to both the lines $\mathrm{L}_1:\frac{x+1}{3}=\frac{y+3}{5}=\frac{z+5}{7}$ and…MediumSingle correct
11 Apr 2023, Shift 2 · Q28Let the line $l : x = \frac{1-y}{-2} = \frac{z-3}{\lambda}$ , $\lambda \in \mathbb{R}$ meet the plane $P : x + 2y + 3z = 4$ at the point…HardNumerical value
26 Jun 2022, Shift 1 · Q14If the two lines $l_1 : \frac{x-2}{3} = \frac{y+1}{-2}, z = 2$ and $l_2 : \frac{x-1}{1} = \frac{2y+3}{\alpha} = \frac{z+5}{2}$ are…MediumSingle correct
27 Jun 2022, Shift 1 · Q14If two straight lines whose direction cosines are given by the relations $l+m-n=0$ , $3l^2+m^2+cnl=0$ are parallel, then the positive value…MediumSingle correct
3 Aug 2021, Shift 2 · Q76Let $L_1$ and $L_2$ be two lines passing through the points $P(b-c, c-a, a-b)$ and $Q\left(\frac{1}{l}, \frac{1}{m}, \frac{1}{n}\right)$ …HardSingle correct
4 Aug 2021, Shift 1 · Q87Maximum number of lines, through the origin which make equal angles with the three coordinate axes in XYZ-space, is ________.EasyNumerical 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.