JEE Main 2024 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 5 April 2024, Shift 1, Maths Q16

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

If the line

\frac{2-x}{3}=\frac{3y-2}{4\lambda+1}=4-z

makes a right angle with the line

\frac{x+3}{3\mu}=\frac{1-2y}{6}=\frac{5-z}{7}

, then

4\lambda+9\mu

is equal to :

(1) $4$
(2) $5$
(3) $6$ Official answer
(4) $13$

Official answer

Option 3

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Lines in 3D
Idea tested: Condition for Perpendicular Lines

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.