JEE Main 2022 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 30 June 2022, Shift 1, Maths Q16

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

The 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}

is equal to :

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

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
27 Aug 2021, Shift 1 · Q73The 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 :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.