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 idea in other shifts

Asked 3× in all

3 Aug 2021, Shift 1 · Q68A plane passes through the points A(1, 2, 3), B(3, 5, 2) and C(2, 1, 5). If P( $a$ , $b$ , $c$ ) be a point such that $a(b + c) = bc$ , then…HardSingle correct
4 Aug 2021, Shift 1 · Q88If the distance between the point $(a, -1, 1)$ $(a>0)$ and the plane passing through the points $(1, -2, 1)$ , $(3, 1, 0)$ and $(2, 0, 1)$ …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.