JEE Main 2023 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 8 April 2023, Shift 2, Maths Q30

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

Let

P_1

be the plane

3x - y - 7z = 11

and

P_2

be the plane passing through the points

(2, -1, 0)

(2, 0, -1)

, and

(5, 1, 1)

. If the foot of the perpendicular drawn from the point

(7, 4, -1)

on the line of intersection of the planes

P_1

and

P_2

(\alpha, \beta, \gamma)

, then

\alpha + \beta + \gamma

is equal to ______.

Official answer

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Planes in 3D
Idea tested: Plane Through Three Points

Same topic in other shifts

All Planes in 3D questions

6 Apr 2023, Shift 1 · Q13If the equation of the plane passing through the line of intersection of the planes $2x-y+z=3$ , $4x-3y+5z+9=0$ and parallel to the line…MediumSingle correct
6 Apr 2023, Shift 1 · Q30Let the image of the point $(1,2,3)$ in the plane $2x-y+z=9$ be Q. If the coordinates of the point R are $(6,10,7)$ , then the square of…MediumNumerical value
11 Apr 2023, Shift 1 · Q2Let $(\alpha, \beta, \gamma)$ be the image of the point $P(2, 3, 5)$ in the plane $2x + y - 3z = 6$ . Then $\alpha + \beta + \gamma$ is…MediumSingle correct
11 Apr 2023, Shift 1 · Q8If equation of the plane that contains the point $(-2, 3, 5)$ and is perpendicular to each of the planes $2x + 4y + 5z = 8$ and…MediumSingle correct
13 Apr 2023, Shift 2 · Q14The plane, passing through the points $(0,-1,2)$ and $(-1,2,1)$ and parallel to the line passing through $(5,1,-7)$ and $(1,-1,-1)$ , also…MediumSingle correct
25 Jul 2022, Shift 1 · Q14Let $P$ be the plane containing the straight line $\frac{x-3}{9}=\frac{y+4}{-1}=\frac{z-7}{-5}$ and perpendicular to the plane containing…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 42 of the 174 JEE Main shifts held from 2017 to 2026.