Let the image of the point $P(1, 2, 6)$ in the plane passing through the points $A(1, 2, 0)$, $B(1, 4, 1)$ and $C(0, 5, 1)$ be $Q(\alpha, \beta, \gamma)$. Then $(\alpha^2 + \beta^2 + \gamma^2)$ is equal to

JEE Main 2023 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 10 April 2023, Shift 2, Maths Q14

Question 14 of 90 in this shift, Maths question 14 of 30, Section A.

Let the image of the point

P(1, 2, 6)

in the plane passing through the points

A(1, 2, 0)

B(1, 4, 1)

and

C(0, 5, 1)

Q(\alpha, \beta, \gamma)

. Then

(\alpha^2 + \beta^2 + \gamma^2)

is equal to

(1) $62$
(2) $65$ Official answer
(3) $70$
(4) $76$

Official answer

Option 2

NTA final key.

Chapter: Three Dimensional Geometry
Topic: Planes in 3D
Idea tested: Image of a Point in a Plane

Same idea in other shifts

Asked 5× in all

6 Apr 2023, Shift 1 · Q30Let the image of the point $(1,2,3)$ in the plane $2x-y+z=9$ be Q. If the coordinates of the point R are $(6,10,7)$ , then the square of…MediumNumerical value
11 Apr 2023, Shift 1 · Q2Let $(\alpha, \beta, \gamma)$ be the image of the point $P(2, 3, 5)$ in the plane $2x + y - 3z = 6$ . Then $\alpha + \beta + \gamma$ is…MediumSingle correct
13 Apr 2023, Shift 1 · Q27Let the image of the point $\left(\frac{5}{3},\frac{5}{3},\frac{8}{3}\right)$ in the plane $x-2y+z-2=0$ be P. If the distance of the point…MediumNumerical value
8 Jan 2020, Shift 2 · Q66The mirror image of the point $(1, 2, 3)$ in a plane is $\left(-\frac{7}{3}, -\frac{4}{3}, -\frac{1}{3}\right)$ . Which of the following…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.