Under what condition are the two lines
`y=m/lx+alpha,z=n/lx+beta, and y=(m')/(l')x+alpha',z=(n')/(l')x+beta'`orthogonal?

Options

A. `alphaalpha'+betabeta'+1=0`
B. `(alpha+alpha')+(beta+beta')=0`
C. `ll'+mm'+nn'=1`
D. `ll'+mm'+nn'=0`

Answer

D

Explanation

Given two lines are : `y=(mx)/l+alpha,z=n/lx+beta and y=(m')/(l')x+alpha',z=(n')/(l')x+beta'`
These two lines can be represented as :
`(y-alpha)/(m//l)=(x-0)/1=(z-beta)/(n//l)and(y-alpha')/(m'//l')=(x-0)/1=(z-beta')/(n'//l')`
They are orthogonal, if
`m/lxx(m')/(l')=1xx1+n/lxx(n')/(l')=-1rArrll'+mm'+n n'=0`