JEE Main 2021 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 27 August 2021, Shift 1, Maths Q73

Question 73 of 90 in this shift, Maths question 13 of 30, Section A.

The distance of the point

(1, -2, 3)

from the plane

x-y+z=5

measured parallel to a line, whose direction ratios are

2, 3, -6

is :

(1) $2$
(2) $3$
(3) $1$ Official answer
(4) $5$

Official answer

Option 3

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Point-Plane Distance
Idea tested: Distance Along a Line

Same idea in other shifts

Asked 9× in all

4 Apr 2026, Shift 1 · Q15The square of the distance of the point $(-2,-8,6)$ from the line $\frac{x-1}{1}=\frac{y-1}{2}=\frac{z}{-1}$ along the line…MediumSingle correct
11 Apr 2023, Shift 2 · Q16Let the line passing through the points $P(2, -1, 2)$ and $Q(5, 3, 4)$ meet the plane $x - y + z = 4$ at the point $R$ . Then the distance…HardSingle correct
13 Apr 2023, Shift 1 · Q17The distance of the point $(-1,2,3)$ from the plane $\vec{r}\cdot\left(\hat{i}-2\hat{j}+3\hat{k}\right)=10$ parallel to the line of the…HardSingle correct
15 Apr 2023, Shift 1 · Q29Let the plane P contain the line $2x+y-z-3=0=5x-3y+4z+9$ and be parallel to the line $\frac{x+2}{2}=\frac{3-y}{-4}=\frac{z-7}{5}$ . Then…HardNumerical value
29 Jul 2022, Shift 1 · Q9If the foot of the perpendicular from the point $A(-1, 4, 3)$ on the plane $P : 2x + my + nz = 4$ , is…MediumSingle correct
30 Jun 2022, Shift 1 · Q16The distance of the point $(3, 2, -1)$ from the plane $3x - y + 4z + 1 = 0$ along the line $\frac{2-x}{2} = \frac{y-3}{2} = \frac{z+1}{1}$ …MediumSingle correct
16 Mar 2021, Shift 2 · Q83If the distance of the point (1, $-2$ , 3) from the plane $x+2y-3z+10=0$ measured parallel to the line,…MediumNumerical value
4 Sep 2020, Shift 2 · Q67The distance of the point $(1, -2, 3)$ from the plane $x-y+z=5$ measured parallel to the line $\frac{x}{2}=\frac{y}{3}=\frac{z}{-6}$ is :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.