JEE Main 2023 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 6 April 2023, Shift 2, Maths Q28

Question 28 of 90 in this shift, Maths question 28 of 30, Section B.

If the lines

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

and

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

intersect, then the magnitude of the minimum value of

8\alpha\beta

is ___________.

Official answer

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Skew Lines
Idea tested: Coplanarity Determinant Test

Same idea in other shifts

Asked 5× in all

12 Apr 2023, Shift 1 · Q15Let the lines $l_1: \frac{x+5}{3}=\frac{y+4}{1}=\frac{z-\alpha}{-2}$ and $l_2: 3x+2y+z-2=0=x-3y+2z-13$ be coplanar. If the point…HardSingle correct
13 Apr 2023, Shift 2 · Q15The line, that is coplanar to the line $\frac{x+3}{-3}=\frac{y-1}{1}=\frac{z-5}{5}$ , isMediumSingle correct
28 Jul 2022, Shift 2 · Q75Let the lines $\frac{x-1}{\lambda}=\frac{y-2}{1}=\frac{z-3}{2}$ and $\frac{x+26}{-2}=\frac{y+18}{3}=\frac{z+28}{\lambda}$ be coplanar and…MediumSingle correct
25 Jul 2021, Shift 2 · Q82If the lines $\frac{x-k}{1}=\frac{y-2}{2}=\frac{z-3}{3}$ and $\frac{x+1}{3}=\frac{y+2}{2}=\frac{z+3}{1}$ are co-planar, then the value of…EasyNumerical value

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.