If the equation of a plane P, passing through the intersection of the planes, $x + 4y - z + 7 = 0$ and $3x + y + 5z = 8$ is $ax + by + 6z = 15$ for some $a, b \in \mathbf{R}$, then the distance of the point $(3, 2, -1)$ from the plane P is ________.

JEE Main 2020 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 4 September 2020, Shift 1, Maths Q74

Question 74 of 75 in this shift, Maths question 24 of 25.

If the equation of a plane P, passing through the intersection of the planes,

x + 4y - z + 7 = 0

and

3x + y + 5z = 8

ax + by + 6z = 15

for some

a, b \in \mathbf{R}

, then the distance of the point

(3, 2, -1)

from the plane P is ________.

Official answer

3.00

NTA final key (Sep 2020).

Chapter: Three Dimensional Geometry
Topic: Planes in 3D
Idea tested: Family of Planes

Same idea in other shifts

Asked 15× in all

6 Apr 2023, Shift 1 · Q13If the equation of the plane passing through the line of intersection of the planes $2x-y+z=3$ , $4x-3y+5z+9=0$ and parallel to the line…MediumSingle correct
6 Apr 2023, Shift 2 · Q15A plane P contains the line of intersection of the plane $\vec{r}\cdot\left(\hat{i}+\hat{j}+\hat{k}\right)=6$ and…MediumSingle correct
13 Apr 2023, Shift 1 · Q8Let the equation of plane passing through the line of intersection of the planes $x+2y+az=2$ and $x-y+z=3$ be $5x-11y+bz=6a-1$ . For…MediumSingle correct
26 Jul 2022, Shift 2 · Q27The plane passing through the line $L: lx-y+3(1-l)z=1,\ x+2y-z=2$ and perpendicular to the plane $3x+2y+z=6$ is $3x-8y+7z=4$ . If $\theta$ …HardNumerical value
27 Jul 2022, Shift 1 · Q17If the plane $P$ passes through the intersection of two mutually perpendicular planes $2x + ky - 5z = 1$ and $3kx - ky + z = 5$ , $k < 3$ …MediumSingle correct
28 Jun 2022, Shift 1 · Q16The acute angle between the planes P $_1$ and P $_2$ , when P $_1$ and P $_2$ are the planes passing through the intersection of the planes…MediumSingle correct
28 Jun 2022, Shift 1 · Q17Let the plane $P:\vec{r}\cdot\vec{a}=d$ contain the line of intersection of two planes…HardSingle correct
26 Aug 2021, Shift 1 · Q75A plane P contains the line $x+2y+3z+1=0=x-y-z-6$ , and is perpendicular to the plane $-2x+y+z+8=0$ . Then which of the following points…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.