JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 29 July 2022, Shift 2, Maths Q14

Question 14 of 90 in this shift, Maths question 14 of 30, Section A.

Let

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 that

\angle PRQ=60^{\mathrm{o}}

, then the area of

\Delta PQR

is equal to :

(1) $\frac{\sqrt{3}}{2}$
(2) $\sqrt{3}$ Official answer
(3) $2\sqrt{3}$
(4) $3$

Official answer

Option 2

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

10 Apr 2023, Shift 2 · Q29Let the foot of perpendicular from the point A $(4, 3, 1)$ on the plane P : $x - y + 2z + 3 = 0$ be N. If B $(5, \alpha, \beta)$ ,…HardNumerical value
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 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.