JEE Main 2026 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 2 April 2026, Shift 2, Maths Q15

Question 15 of 75 in this shift, Maths question 15 of 25, Section A.

Let the point

A

be the foot of perpendicular drawn from the point

P(a, b, 0)

on the line

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

. If the midpoint of the line segment

PA

\left(0, \frac{3}{4}, -\frac{1}{4}\right)

, then the value of

a^2 + b^2 + \alpha^2

is equal to:

(1) $1$ Official answer
(2) $2$
(3) $6$
(4) $9$

Official answer

Option 1

NTA final key.

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

Same idea in other shifts

Asked 6× in all

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

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 42 of the 174 JEE Main shifts held from 2017 to 2026.