PrepRung
Sign inSign up free

JEE Advanced 2016 Paper 1 · Mathematics · Three Dimensional Geometry · medium

The plane Pi contains the line (x-1)/(2)=y/1=(z+1)/(-1) and the point (0,1,2). The sum of the coordinates of the mirror image of the point (3,-1,2)…

Single correct option

The plane Π\Pi contains the line x−12=y1=z+1−1\dfrac{x-1}{2}=\dfrac{y}{1}=\dfrac{z+1}{-1} and the point (0,1,2)(0,1,2). The sum of the coordinates of the mirror image of the point (3,−1,2)(3,-1,2) in Π\Pi is
  1. A. 7825\dfrac{78}{25}
  2. B. 22
  3. C. 5625\dfrac{56}{25}
  4. D. 12425\dfrac{124}{25}
Show answer and solution

Answer: (C) 5625\dfrac{56}{25}

The line passes through A(1,0,−1)A(1,0,-1) with direction d⃗=(2,1,−1)\vec d=(2,1,-1). A normal to Π\Pi is d⃗×AP→\vec d\times\overrightarrow{AP} with P(0,1,2)P(0,1,2), i.e. (2,1,−1)×(−1,1,3)=(4,−5,3)(2,1,-1)\times(-1,1,3)=(4,-5,3). The plane is 4x−5y+3z−1=04x-5y+3z-1=0, and PP satisfies it. For Q(3,−1,2)Q(3,-1,2) the expression is 12+5+6−1=2212+5+6-1=22 and ∣n⃗∣2=50|\vec n|^2=50. The image is Q′=Q−2⋅2250(4,−5,3)=(3−8825, −1+225, 2−6625)=(−1325,175,−1625)Q'=Q-\dfrac{2\cdot22}{50}(4,-5,3)=\left(3-\tfrac{88}{25},\,-1+\tfrac{22}{5},\,2-\tfrac{66}{25}\right)=\left(-\tfrac{13}{25},\tfrac{17}{5},-\tfrac{16}{25}\right). The option 78/2578/25 is the sum for the foot of the perpendicular, not the image.
Report a mistake

Original question written in the JEE Advanced 2016 Paper 1 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake