Under what condition are the two linesy=mℓx+α,z=nℓx+β; and y=m′ℓ′x | Filo
filo Logodropdown-logo

Class 12

Math

3D Geometry

Three Dimensional Geometry

view icon556
like icon150

Under what condition are the two linesy=mℓx+α,z=nℓx+β; and y=m′ℓ′x+α′,z=n′ℓ′x+β′ Orthogonal?

  1. αα′+ββ′+1=0
  2. (α+α′)+(β+β′)=0
  3. ℓℓ′+mm′+nn′=1
  4. ℓℓ′+mm′+nn′=0
Correct Answer: Option(d)
Solution: [d] Given two lines are: y=mxℓ+α,z=nℓx+β and y=m′ℓ′x+α′,z=n′ℓ′x+β′ These two lines can be represented as: y−αm/ℓ=x−01=z−βn/ℓ And y−α′m′/c′=x−01=z−β′n′/ℓ′ They are orthogonal, if mℓ×m′ℓ′+1×1+nℓn′ℓ′=−1⇒ℓℓ′+mm′+nn′=0
view icon556
like icon150
filo banner image

Connecting you to a tutor in 60 seconds.

Get answers to your doubts.

playstore logoplaystore logo
Similar Topics
three dimensional geometry
different products of vectors and their geometrical applications
three-dimensional geometry
vector algebra
conic sections