JEE Main 2026 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 6 April 2026, Shift 1, Maths Q15

Question 15 of 75 in this shift, Maths question 15 of 25, Section A.

Let the image of the point

\mathrm{P}(1,6,a)

in the line

\mathrm{L}:\frac{x}{1}=\frac{y-1}{2}=\frac{z-a+1}{b}

b>0

, be

\left(\frac{a}{3},0,a+c\right)

. If

\mathrm{S}(\alpha,\beta,\gamma)

\alpha>0

, is the point on L such that the distance of S from the foot of perpendicular from the point P on L is

2\sqrt{14}

, then

\alpha+\beta+\gamma

is equal to:

(1)19
(2)20
(3)21Official answer
(4)22

Official answer

Option 3

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Lines in 3D
Idea tested: Image of a Point in a Line

Same idea in other shifts

Asked 16× in all

4 Apr 2026, Shift 2 · Q14If $\left(2\alpha+1,\,\alpha^2-3\alpha,\,\frac{\alpha-1}{2}\right)$ is the image of $(\alpha,2\alpha,1)$ in the line…MediumSingle correct
5 Apr 2026, Shift 2 · Q15If the distance of the point $(a, 2, 5)$ from the image of the point $(1, 2, 7)$ in the line $\frac{x}{1}=\frac{y-1}{1}=\frac{z-2}{2}$ is…MediumSingle correct
6 Apr 2026, Shift 2 · Q24Let the image of the point P $(0,-5,0)$ in the line $\frac{x-1}{2}=\frac{y}{1}=\frac{z+1}{-2}$ be the point R and the image of the point…HardNumerical value
2 Apr 2025, Shift 2 · Q14If the image of the point $P(1, 0, 3)$ in the line joining the points $A(4, 7, 1)$ and $B(3, 5, 3)$ is $Q(\alpha, \beta, \gamma)$ , then…MediumSingle correct
4 Apr 2024, Shift 2 · Q29Consider a line L passing through the points $P(1,2,1)$ and $Q(2,1,-1)$ . If the mirror image of the point $A(2,2,2)$ in the line L is…MediumNumerical value
5 Apr 2024, Shift 2 · Q17Let $(\alpha, \beta, \gamma)$ be the image of the point $(8, 5, 7)$ in the line $\frac{x-1}{2} = \frac{y+1}{3} = \frac{z-2}{5}$ . Then…MediumSingle correct
6 Apr 2024, Shift 2 · Q17Let $P(\alpha,\beta,\gamma)$ be the image of the point $Q(3,-3,1)$ in the line $\frac{x-0}{1}=\frac{y-3}{1}=\frac{z-1}{-1}$ and $R$ be the…HardSingle correct
8 Apr 2024, Shift 2 · Q29Let $P(\alpha, \beta, \gamma)$ be the image of the point $Q(1, 6, 4)$ in the line $\frac{x}{1} = \frac{y-1}{2} = \frac{z-2}{3}$ . Then…MediumNumerical value

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.