The equation of the line through the point 0 , 1 , 2 and perpendicular to the line x - 1 2 = y + 1 3 = z - 1…

The equation of the line through the point 0,1,2 and perpendicular to the line x-12=y+13=z-1-2 is :
  1. x3=y-1-4=z-23
  2. x3=y-14=z-23
  3. x-3=y-14=z-23
  4. x3=y-14=z-2-3

Solution

x-12=y+13=z-1-2=r

⇒ Px,y,z=2r+1,3r-1,-2r+1

Since, QP→⊥2i^+3j^-2k^

⇒ 4r+2+9r-6+4r+2=0

⇒ r=217

⇒ P2117,-1117,1317

⇒ PQ→=21i^-28j^-21k^17

So, QP→:x-3=y-14=z-23

Asked in: JEE Main 2021 (25 Feb Shift 1)

Practice more Line and Plane questions on Aicharya