JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 26 February 2021, Shift 2, Maths Q76

Question 76 of 90 in this shift, Maths question 16 of 30, Section A.

Let 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 perpendicular from

(3, 2, 1)

on L, then the value of

21(\alpha+\beta+\gamma)

equals :

(1) $68$
(2) $102$ Official answer
(3) $136$
(4) $142$

Official answer

Option 2

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
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
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.