JEE Main 2021 · MathsMultiple choiceSingle correctEasyCalculation

JEE Main 24 February 2021, Shift 1, Maths Q77

Question 77 of 90 in this shift, Maths question 17 of 30, Section A.

The distance of the point

(1, 1, 9)

from the point of intersection of the line

\frac{x - 3}{1} = \frac{y - 4}{2} = \frac{z - 5}{2}

and the plane

x + y + z = 17

is :

(1) $2\sqrt{19}$
(2) $19\sqrt{2}$
(3) $\sqrt{38}$ Official answer
(4) $38$

Official answer

Option 3

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Planes in 3D
Idea tested: Intersection Point of Line and Plane

Same idea in other shifts

Asked 3× in all

27 Jul 2022, Shift 1 · Q23Let the line $\dfrac{x-3}{7} = \dfrac{y-2}{-1} = \dfrac{z-3}{-4}$ intersect the plane containing the lines…HardNumerical value
3 Aug 2021, Shift 1 · Q75The distance of the origin from the point of intersection of the line, $\frac{x}{2} = \frac{y + 1}{3} = \frac{z - 1}{-1}$ and the plane,…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 108 of the 174 JEE Main shifts held from 2017 to 2026.