JEE Main 2023 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 11 April 2023, Shift 2, Maths Q15

Question 15 of 90 in this shift, Maths question 15 of 30, Section A.

Let

P

be the plane passing through the points

(5,3,0)

(13,3,-2)

and

(1,6,2)

. For

\alpha \in \mathbb{N}

, if the distances of the points

A(3, 4, \alpha)

and

B(2, \alpha, a)

from the plane

P

are

2

and

3

respectively, then the positive value of

a

(1) $3$
(2) $4$ Official answer
(3) $5$
(4) $6$

Official answer

Option 2

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Point-Plane Distance
Idea tested: Distance to Plane Through Three Points

Same topic in other shifts

All Point-Plane Distance questions

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
8 Apr 2023, Shift 1 · Q28Let $\lambda_1,\lambda_2$ be the values of $\lambda$ for which the points $\left(\frac{5}{2},1,\lambda\right)$ and $(-2,0,1)$ are at equal…MediumNumerical value
10 Apr 2023, Shift 1 · Q13Let two vertices of a triangle ABC be $(2,4,6)$ and $(0,-2,-5)$ , and its centroid be $(2,1,-1)$ . If the image of the third vertex in the…MediumSingle correct
10 Apr 2023, Shift 1 · Q14Let P be the point of intersection of the line $\frac{x+3}{3}=\frac{y+2}{1}=\frac{1-z}{2}$ and the plane $x+y+z=2$ . If the distance of the…MediumSingle correct
10 Apr 2023, Shift 2 · Q29Let the foot of perpendicular from the point A $(4, 3, 1)$ on the plane P : $x - y + 2z + 3 = 0$ be N. If B $(5, \alpha, \beta)$ ,…HardNumerical value
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

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.