JEE Main 2020 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 5 September 2020, Shift 1, Maths Q66

Question 66 of 75 in this shift, Maths question 16 of 25.

If (a, b, c) is the image of the point (1, 2,

-3

) in the line,

\frac{x+1}{2}=\frac{y-3}{-2}=\frac{z}{-1}

, then a + b + c is equal to :

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

Official answer

Option 3

NTA final key (Sep 2020).

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 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
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

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.