JEE Main 2023 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 8 April 2023, Shift 1, Maths Q15

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

If the equation of the plane containing the line

x+2y+3z-4=0=2x+y-z+5

and perpendicular to the plane

\vec{r}=(\hat{i}-\hat{j})+\lambda(\hat{i}+\hat{j}+\hat{k})+\mu(\hat{i}-2\hat{j}+3\hat{k})

ax+by+cz=4

, then

(a-b+c)

is equal to

(1) $18$
(2) $20$
(3) $22$ Official answer
(4) $24$

Official answer

Option 3

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Planes in 3D
Idea tested: Family of Planes Perpendicular to a Third Plane

Same idea in other shifts

Asked 5× in all

12 Apr 2023, Shift 1 · Q14Let the plane P: $4x-y+z=10$ be rotated by an angle $\frac{\pi}{2}$ about its line of intersection with the plane $x+y-z=4$ . If $\alpha$ …HardSingle correct
26 Jun 2022, Shift 1 · Q15Let the plane $2x + 3y + z + 20 = 0$ be rotated through a right angle about its line of intersection with the plane $x - 3y + 5z = 8$ . If…HardSingle correct
26 Jun 2022, Shift 2 · Q14If the plane $2x + y - 5z = 0$ is rotated about its line of intersection with the plane $3x - y + 4z - 7 = 0$ by an angle of…MediumSingle correct
4 Aug 2021, Shift 2 · Q76The distance of the point $(5,6,9)$ from the plane, which passes through the line of intersection of the planes $x+y-z=1$ and…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.