Find the Cartesian equations of the line which passes through the point (–2, 4, –5) and is parallel to the line

The equation of the given line is,

It can be re-written as,

Since the required line is parallel to the given line, the direction ratios of the required line are proportional to 3, -5, 6.

Hence, the Cartesian equations of the line passing through the point (-2, 4, -5) and parallel to a vector having direction

ratios proportional to 3, -5, 6 is →