If the length of the perpendicular drawn from the point P(a, 4, 2), a > 0 on the line $\frac{x+1}{2} = \frac{y-3}{3} = \frac{z-1}{-1}$ is $2\sqrt{6}$ units and $Q(\alpha_1, \alpha_2, \alpha_3)$ is the image of the point P in this line, then $a + \sum_{i=1}^{3} \alpha_i$ is equal to :

JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 27 July 2022, Shift 2, Maths Q14

Question 14 of 90 in this shift, Maths question 14 of 30, Section A.

If the length of the perpendicular drawn from the point P(a, 4, 2), a > 0 on the line

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

2\sqrt{6}

units and

Q(\alpha_1, \alpha_2, \alpha_3)

is the image of the point P in this line, then

a + \sum_{i=1}^{3} \alpha_i

is equal to :

(1) $7$
(2) $8$ Official answer
(3) $12$
(4) $14$

Official answer

Option 2

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 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.