JEE Main 2021 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 25 February 2021, Shift 1, Maths Q74

Question 74 of 90 in this shift, Maths question 14 of 30, Section A.

The equation of the line through the point (0, 1, 2) and perpendicular to the line

\frac{x-1}{2} = \frac{y+1}{3} = \frac{z-1}{-2}

is :

(1) $\frac{x}{3} = \frac{y-1}{4} = \frac{z-2}{-3}$
(2) $\frac{x}{-3} = \frac{y-1}{4} = \frac{z-2}{3}$ Official answer
(3) $\frac{x}{3} = \frac{y-1}{-4} = \frac{z-2}{3}$
(4) $\frac{x}{3} = \frac{y-1}{4} = \frac{z-2}{3}$

Official answer

Option 2

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Lines in 3D
Idea tested: Cartesian Symmetric Form

Same topic in other shifts

All Lines in 3D questions

2 Apr 2026, Shift 1 · Q13If the point of intersection of the lines $\frac{x+1}{3}=\frac{y+a}{5}=\frac{z+b+1}{7}$ and $\frac{x-2}{1}=\frac{y-b}{4}=\frac{z-2a}{7}$ …MediumSingle correct
2 Apr 2026, Shift 1 · Q15Let a line L passing through the point $(1, 1, 1)$ be perpendicular to both the vectors $2\hat i+2\hat j+\hat k$ and…MediumSingle correct
2 Apr 2026, Shift 2 · Q15Let the point $A$ be the foot of perpendicular drawn from the point $P(a, b, 0)$ on the line…MediumSingle correct
4 Apr 2026, Shift 1 · Q14A line with direction ratios $1,-1,2$ intersects the lines $\frac{x}{2}=\frac{y}{3}=\frac{z+1}{3}$ and…MediumSingle correct
4 Apr 2026, Shift 2 · Q14If $\left(2\alpha+1,\,\alpha^2-3\alpha,\,\frac{\alpha-1}{2}\right)$ is the image of $(\alpha,2\alpha,1)$ in the line…MediumSingle correct
5 Apr 2026, Shift 1 · Q13The square of the distance of the point $P(5, 6, 7)$ from the line $\frac{x-2}{2}=\frac{y-5}{3}=\frac{z-2}{4}$ 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.