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 12× 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
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
30 Jan 2024, Shift 1 · Q16Let $(\alpha,\beta,\gamma)$ be the foot of perpendicular from the point $(1,2,3)$ on the line $\frac{x+3}{5}=\frac{y-1}{2}=\frac{z+4}{3}$ .…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
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.