JEE Main 2026 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 5 April 2026, Shift 2, Maths Q15

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

If 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 4, then the sum of all possible values of a is equal to :

(1) $11$
(2) $9$
(3) $6$ Official answer
(4) $4$

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 8× 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
6 Apr 2026, Shift 1 · Q15Let 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…HardSingle 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
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
9 Apr 2024, Shift 2 · Q29The square of the distance of the image of the point $(6, 1, 5)$ in the line $\frac{x-1}{3}=\frac{y}{2}=\frac{z-2}{4}$ , from the origin is…MediumNumerical value
31 Jan 2024, Shift 2 · Q16Let $(\alpha,\beta,\gamma)$ be the mirror image of the point $(2,3,5)$ in the line $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ . Then,…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 42 of the 174 JEE Main shifts held from 2017 to 2026.