JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 27 July 2022, Shift 1, Maths Q23

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

Let the line

\dfrac{x-3}{7} = \dfrac{y-2}{-1} = \dfrac{z-3}{-4}

intersect the plane containing the lines

\dfrac{x-4}{1} = \dfrac{y+1}{-2} = \dfrac{z}{1}

and

4ax - y + 5z - 7a = 0 = 2x - 5y - z - 3

a \in \mathbb{R}

at the point

P(\alpha, \beta, \gamma)

. Then the value of

\alpha + \beta + \gamma

equals ________.

Official answer

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Planes in 3D
Idea tested: Intersection Point of Line and Plane

Same idea in other shifts

Asked 3× in all

3 Aug 2021, Shift 1 · Q75The distance of the origin from the point of intersection of the line, $\frac{x}{2} = \frac{y + 1}{3} = \frac{z - 1}{-1}$ and the plane,…MediumSingle correct
24 Feb 2021, Shift 1 · Q77The distance of the point $(1, 1, 9)$ from the point of intersection of the line $\frac{x - 3}{1} = \frac{y - 4}{2} = \frac{z - 5}{2}$ and…EasySingle 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.