It is given that the line passes through the point
(−2,4,−5) and
is parallel to
x+33=y−45=z+86 ....(1)
The direction ratios of the line (1) are
3,5 and
6.
The required line is parallel to equation (1).
Therefore, its direction ratios are 3k,5k and 6k, where k≠0.
It
is known that the equation of the line through the point (x1,y1,z1) and with direction ratios, a,b,c is given by
x−x1a=y−y1b=z−z1c
Therefore, the equation of the required line is,
x+23k=y−45k=z+56k
⇒ x+23=y−45=z+56