Question

If l, m, n are lines such that I ||
are lines such that I || m and m || n, then show that l|| n.
. ​

Answer 1

Proof ( Using lines' equations ) :

Let, the equation of the line l is

ax + by = c, .....(i)

where a, b and c are arbitrary constants

Since, l || m, the equation of m can be taken as

ax + by = d, .....(ii)

where d is arbitrary

Since, m || n, the equation of n can be taken as

ax + by = e, .....(iii)

where e is arbitrary

From (i) and (iii), we can conclude that the equations are of parallel lines,

i.e., m || n

This completes the proof.