JEE Main 2024 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 30 January 2024, Shift 1, Maths Q16

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

Let

(\alpha,\beta,\gamma)

be the foot of perpendicular from the point

(1,2,3)

on the line

\frac{x+3}{5}=\frac{y-1}{2}=\frac{z+4}{3}

. Then

19(\alpha+\beta+\gamma)

is equal to :

(1) $99$
(2) $100$
(3) $101$ Official answer
(4) $102$

Official answer

Option 3

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Lines in 3D
Idea tested: Foot of the Perpendicular

Same idea in other shifts

Asked 12× in all

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
5 Apr 2026, Shift 2 · Q14Let a triangle PQR be such that P and Q lie on the line $\frac{x+3}{8}=\frac{y-4}{2}=\frac{z+1}{2}$ and are at a distance of 6 units from…MediumSingle correct
6 Apr 2024, Shift 1 · Q28Let $P$ be the point $(10,-2,-1)$ and $Q$ be the foot of the perpendicular drawn from the point $R(1,7,6)$ on the line passing through the…MediumNumerical value
31 Jan 2024, Shift 1 · Q29Let Q and R be the feet of perpendiculars from the point $P(a,a,a)$ on the lines $x=y,\ z=1$ and $x=-y,\ z=-1$ respectively. If…MediumNumerical value
13 Apr 2023, Shift 2 · Q16Let N be the foot of perpendicular from the point P $(1,-2,3)$ on the line passing through the points $(4,5,8)$ and $(1,-7,5)$ . Then the…MediumSingle correct
27 Jun 2022, Shift 2 · Q13Let the foot of the perpendicular from the point $(1, 2, 4)$ on the line $\frac{x+2}{4}=\frac{y-1}{2}=\frac{z+1}{3}$ be $P$ . Then the…MediumSingle correct
26 Feb 2021, Shift 2 · Q76Let L be a line obtained from the intersection of two planes $x+2y+z=6$ and $y+2z=4$ . If point $P(\alpha, \beta, \gamma)$ is the foot of…MediumSingle correct
22 Jul 2021, Shift 2 · Q69Let $\mathrm{L}$ be the line of intersection of planes $\vec{\mathrm{r}}\cdot(\hat{i}-\hat{j}+2\hat{k})=2$ and…MediumSingle 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.