JEE Main 2023 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 10 April 2023, Shift 2, Maths Q29

Question 29 of 90 in this shift, Maths question 29 of 30, Section B.

Let the foot of perpendicular from the point A

(4, 3, 1)

on the plane P :

x - y + 2z + 3 = 0

be N. If B

(5, \alpha, \beta)

\alpha, \beta \in \mathbb{Z}

is a point on plane P such that the area of the triangle ABN is

3\sqrt{2}

, then

\alpha^2 + \beta^2 + \alpha\beta

is equal to ___________.

Official answer

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Point-Plane Distance
Idea tested: Foot of Perpendicular

Same idea in other shifts

Asked 5× in all

28 Jul 2022, Shift 1 · Q16The foot of the perpendicular from a point on the circle $x^2+y^2=1,\ z=0$ to the plane $2x+3y+z=6$ lies on which one of the following…HardSingle correct
29 Jul 2022, Shift 2 · Q14Let $Q$ be the foot of perpendicular drawn from the point $P\,(1, 2, 3)$ to the plane $x+2y+z=14$ . If $R$ is a point on the plane such…MediumSingle correct
29 Jun 2022, Shift 1 · Q23Let $d$ be the distance between the foot of perpendiculars of the points $P(1, 2, -1)$ and $Q(2, -1, 3)$ on the plane $-x + y + z = 1$ .…MediumNumerical value
26 Aug 2021, Shift 2 · Q89Let Q be the foot of the perpendicular from the point $\mathrm{P}(7,-2,13)$ on the plane containing the lines…HardNumerical 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.