JEE Main 2017 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 2 April 2017 (offline), Maths Q83

Question 83 of 90 in this shift, Maths question 23 of 30.

If 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}

is Q, then PQ is equal to :

(1) $2\sqrt{42}$ Official answer
(2) $\sqrt{42}$
(3) $6\sqrt{5}$
(4) $3\sqrt{5}$

Official answer

Option 1

CBSE answer key (25/04/2017, used for result).

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
27 Jun 2022, Shift 1 · Q30Let 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…MediumNumerical value
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

Question text from the official JEE Main paper published by NTA (CBSE ran the 2017 exam); 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.