JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 25 July 2021, Shift 1, Maths Q69

Question 69 of 90 in this shift, Maths question 9 of 30, Section A.

Let the foot of perpendicular from a point P(1, 2,

-1

) to the straight line

L:\frac{x}{1}=\frac{y}{0}=\frac{z}{-1}

be N. Let a line be drawn from P parallel to the plane

x+y+2z=0

which meets L at point Q. If

\alpha

is the acute angle between the lines PN and PQ, then

\cos\alpha

is equal to _________.

(1) $\frac{\sqrt3}{2}$
(2) $\frac{1}{\sqrt3}$ Official answer
(3) $\frac{1}{\sqrt5}$
(4) $\frac{1}{2\sqrt3}$

Official answer

Option 2

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Lines in 3D
Idea tested: Foot of the Perpendicular

Same idea in other shifts

Asked 6× in all

2 Apr 2026, Shift 2 · Q15Let the point $A$ be the foot of perpendicular drawn from the point $P(a, b, 0)$ on the line…MediumSingle correct
5 Apr 2026, Shift 2 · Q14Let a triangle PQR be such that P and Q lie on the line $\frac{x+3}{8}=\frac{y-4}{2}=\frac{z+1}{2}$ and are at a distance of 6 units from…MediumSingle correct
31 Jan 2024, Shift 1 · Q29Let Q and R be the feet of perpendiculars from the point $P(a,a,a)$ on the lines $x=y,\ z=1$ and $x=-y,\ z=-1$ respectively. If…MediumNumerical value
13 Apr 2023, Shift 2 · Q16Let N be the foot of perpendicular from the point P $(1,-2,3)$ on the line passing through the points $(4,5,8)$ and $(1,-7,5)$ . Then the…MediumSingle correct
16 Mar 2021, Shift 2 · Q61If the foot of the perpendicular from point (4, 3, 8) on the line $L_1:\frac{x-a}{l}=\frac{y-2}{3}=\frac{z-b}{4}$ , $l\neq0$ is (3, 5, 7),…MediumSingle 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 42 of the 174 JEE Main shifts held from 2017 to 2026.