Let the foot of perpendicular of the point $P(3,-2,-9)$ on the plane passing through the points $(-1,-2,-3)$, $(9,3,4)$, $(9,-2,1)$ be $Q(\alpha,\beta,\gamma)$. Then the distance of $Q$ from the origin is

JEE Main 2023 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 15 April 2023, Shift 1, Maths Q14

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

Let the foot of perpendicular of the point

P(3,-2,-9)

on the plane passing through the points

(-1,-2,-3)

(9,3,4)

(9,-2,1)

Q(\alpha,\beta,\gamma)

. Then the distance of

Q

from the origin is

(1) $\sqrt{35}$
(2) $\sqrt{38}$
(3) $\sqrt{29}$
(4) $\sqrt{42}$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Planes in 3D
Idea tested: Foot of Perpendicular to a Plane

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
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6 Apr 2023, Shift 2 · Q15A plane P contains the line of intersection of the plane $\vec{r}\cdot\left(\hat{i}+\hat{j}+\hat{k}\right)=6$ and…MediumSingle correct
8 Apr 2023, Shift 1 · Q15If the equation of the plane containing the line $x+2y+3z-4=0=2x+y-z+5$ and perpendicular to the plane…MediumSingle correct
8 Apr 2023, Shift 2 · Q13Let $P$ be the plane passing through the line $\frac{x-1}{1} = \frac{y-2}{-3} = \frac{z+5}{7}$ and the point $(2, 4, -3)$ . If the image of…MediumSingle correct
8 Apr 2023, Shift 2 · Q14For $a, b \in \mathbb{Z}$ and $|a - b| \leq 10$ , let the angle between the plane $P: ax + y - z = b$ and the line…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 108 of the 174 JEE Main shifts held from 2017 to 2026.