JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 25 February 2021, Shift 2, Maths Q73

Question 73 of 90 in this shift, Maths question 13 of 30, Section A.

A plane passes through the points A(1, 2, 3), B(2, 3, 1) and C(2, 4, 2). If O is the origin and P is

(2, -1, 1)

, then the projection of

\overrightarrow{OP}

on this plane is of length :

(1) $\sqrt{\frac{2}{3}}$
(2) $\sqrt{\frac{2}{11}}$ Official answer
(3) $\sqrt{\frac{2}{7}}$
(4) $\sqrt{\frac{2}{5}}$

Official answer

Option 2

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Planes in 3D
Idea tested: Projection of Line Segment on 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
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
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.