JEE Main 2021 · MathsNumerical answerNumerical valueEasyCalculation

JEE Main 18 March 2021, Shift 1, Maths Q85

Question 85 of 90 in this shift, Maths question 25 of 30, Section B.

Let the plane

ax+by+cz+d=0

bisect the line joining the points

(4,-3,1)

and

(2,3,-5)

at the right angles. If a, b, c, d are integers, then the minimum value of

(a^2+b^2+c^2+d^2)

is __________.

Official answer

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Planes in 3D
Idea tested: Perpendicular Bisector Plane

Same idea in other shifts

Asked 3× in all

24 Jun 2022, Shift 2 · Q15Let the points on the plane P be equidistant from the points $(-4, 2, 1)$ and $(2, -2, 3)$ . Then the acute angle between the plane P and…MediumSingle correct
3 Sep 2020, Shift 2 · Q66The plane which bisects the line joining the points $(4, -2, 3)$ and $(2, 4, -1)$ at right angles also passes through the point :EasySingle 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.