Let 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 $P(a,b,c)$ on $l_1$ is nearest to the point $Q(-4,-3,2)$, then $|a|+|b|+|c|$ is equal to

JEE Main 2023 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 12 April 2023, Shift 1, Maths Q15

Question 15 of 90 in this shift, Maths question 15 of 30, Section A.

Let 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

P(a,b,c)

l_1

is nearest to the point

Q(-4,-3,2)

, then

|a|+|b|+|c|

is equal to

(1) $8$
(2) $10$ Official answer
(3) $12$
(4) $14$

Official answer

Option 2

NTA final key.

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

Same idea in other shifts

Asked 5× in all

6 Apr 2023, Shift 2 · Q28If 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…HardNumerical value
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.