Let the mirror image of the point $(a, b, c)$ with respect to the plane $3x-4y+12z+19=0$ be $(a-6, \beta, \gamma)$. If $a+b+c=5$, then $7\beta-9\gamma$ is equal to ____________.

JEE Main 2022 · MathsNumerical answerNumerical valueMediumCalculation

JEE Main 27 June 2022, Shift 1, Maths Q30

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

Let the mirror image of the point

(a, b, c)

with respect to the plane

3x-4y+12z+19=0

(a-6, \beta, \gamma)

. If

a+b+c=5

, then

7\beta-9\gamma

is equal to ____________.

Official answer

137

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Point-Plane Distance
Idea tested: Image of a Point

Same idea in other shifts

Asked 8× in all

10 Apr 2023, Shift 1 · Q13Let two vertices of a triangle ABC be $(2,4,6)$ and $(0,-2,-5)$ , and its centroid be $(2,1,-1)$ . If the image of the third vertex in the…MediumSingle correct
25 Jun 2022, Shift 1 · Q17Let Q be the mirror image of the point P(1, 0, 1) with respect to the plane S : $x+y+z=5$ . If a line L passing through $(1,-1,-1)$ ,…MediumSingle correct
29 Jun 2022, Shift 1 · Q3If the mirror image of the point $(2, 4, 7)$ in the plane $3x - y + 4z = 2$ is $(a, b, c)$ , then $2a + b + 2c$ is equal to :EasySingle correct
27 Aug 2021, Shift 2 · Q87Let S be the mirror image of the point $Q(1, 3, 4)$ with respect to the plane $2x - y + z + 3 = 0$ and let $R(3, 5, \gamma)$ be a point of…MediumNumerical value
26 Feb 2021, Shift 2 · Q61If the mirror image of the point $(1, 3, 5)$ with respect to the plane $4x-5y+2z=8$ is $(\alpha, \beta, \gamma)$ , then…EasySingle correct
18 Mar 2021, Shift 2 · Q88Let the mirror image of the point $(1, 3, a)$ with respect to the plane $\vec{r}\cdot\left(2\hat{i}-\hat{j}+\hat{k}\right)-b=0$ be…MediumNumerical value
2 Apr 2017 (offline) · Q83If the image of the point $P(1,-2,3)$ in the plane, $2x+3y-4z+22=0$ measured parallel to the line, $\frac{x}{1}=\frac{y}{4}=\frac{z}{5}$ …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.