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I suppose there is a mistake in typing in the last equation... it is (z-3)/-6 ?? minus sign is missing ??

L1: x/1 = y/2 = z/3 = m (let's say)

x = m, y = 2m , z = 3 m

or

L2: (x-1)/-2 = (y-2) /-4 = (x-3)/-6 = n

x = 1 - 2n , y = 2 - 4n = 2 (1- 2n) and z = 3 - 6 n = 3 (1 - 2n)

or

Hence both represent the same straight line in 3 dimensional space. They can represent two parallel straightlines in 3-d space.

L1: x/1 = y/2 = z/3 = m (let's say)

x = m, y = 2m , z = 3 m

or

*6 x = 3 y = 2 z*L2: (x-1)/-2 = (y-2) /-4 = (x-3)/-6 = n

x = 1 - 2n , y = 2 - 4n = 2 (1- 2n) and z = 3 - 6 n = 3 (1 - 2n)

or

*6 x = 3 y = 2 z*Hence both represent the same straight line in 3 dimensional space. They can represent two parallel straightlines in 3-d space.