JEE Main Maths · Three Dimensional Geometry

Foot of the Perpendicular

Foot of the Perpendicular (Three Dimensional Geometry) was asked 6 times in 6 JEE Main shifts, 2021–2026, out of the 42 shifts Lumi analysed. 1 of the 6 had a numerical answer.

Times asked: 6; in 6 shifts
Years: 2021–2026
Usual format: Single correct; Multi-step
Pattern: Frequent; repeats across shifts

How it is asked

Foot of perpendicular with midpoint condition
Centroid of triangle with vertices on 3d line

Difficulty

Easy 0Medium 6Hard 0

Where it sits

Chapter: Three Dimensional Geometry. Topic: Lines in 3D, 39 questions over 14 ideas.

All 6 questions

Newest first, each with its options and official answer.

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
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
25 Jul 2021, Shift 1 · Q69Let the foot of perpendicular from a point P(1, 2, $-1$ ) to the straight line $L:\frac{x}{1}=\frac{y}{0}=\frac{z}{-1}$ be N. Let a line be…MediumSingle correct
16 Mar 2021, Shift 2 · Q61If the foot of the perpendicular from point (4, 3, 8) on the line $L_1:\frac{x-a}{l}=\frac{y-2}{3}=\frac{z-b}{4}$ , $l\neq0$ is (3, 5, 7),…MediumSingle correct