JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 29 July 2022, Shift 1, Maths Q23

Question 23 of 90 in this shift, Maths question 23 of 30, Section B.

Let a line with direction ratios

a, -4a, -7

be perpendicular to the lines with direction ratios

3, -1, 2b

and

b, a, -2

. If the point of intersection of the line

\frac{x + 1}{a^2 + b^2} = \frac{y - 2}{a^2 - b^2} = \frac{z}{1}

and the plane

x - y + z = 0

(\alpha, \beta, \gamma)

, then

\alpha + \beta + \gamma

is equal to __________.

Official answer

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Lines in 3D
Idea tested: Point of Intersection Calculation

Same idea in other shifts

Asked 8× in all

2 Apr 2026, Shift 1 · Q13If the point of intersection of the lines $\frac{x+1}{3}=\frac{y+a}{5}=\frac{z+b+1}{7}$ and $\frac{x-2}{1}=\frac{y-b}{4}=\frac{z-2a}{7}$ …MediumSingle correct
4 Apr 2025, Shift 2 · Q15Let A be the point of intersection of the lines $L_1:\frac{x-7}{1}=\frac{y-5}{0}=\frac{z-3}{-1}$ and…MediumSingle correct
5 Apr 2024, Shift 1 · Q17Let d be the distance of the point of intersection of the lines $\frac{x+6}{3}=\frac{y}{2}=\frac{z+1}{1}$ and…MediumSingle correct
29 Jan 2024, Shift 1 · Q16Let PQR be a triangle with $R(-1,4,2)$ . Suppose $M(2,1,2)$ is the mid point of PQ. The distance of the centroid of $\Delta PQR$ from the…MediumSingle correct
10 Apr 2023, Shift 2 · Q15Let the line $\frac{x}{1} = \frac{6-y}{2} = \frac{z+8}{5}$ intersect the lines $\frac{x-5}{4} = \frac{y-7}{3} = \frac{z+2}{1}$ and…HardSingle correct
4 Aug 2021, Shift 2 · Q75The equation of a line passing through the point $(2,-1,1)$ and the point of intersection of the lines $2x-y-4=0=y+2z$ and…MediumSingle correct
31 Aug 2021, Shift 1 · Q87The square of the distance of the point of intersection of the line $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z+1}{6}$ and the plane $2x-y+z=6$ …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.