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

Class 12

Math

3D Geometry

Three Dimensional Geometry

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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
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
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