Parallel Lines

The given line is represented by the equation:

This line passes through the point and has the direction vector . A line parallel to this line will have the same direction vector.
The requirement is to find the line passing through the origin and parallel to .
Hence, the equation of a line through the origin with direction vector is:

Expressed parametrically, this is:
(This matches choice (A)).
Additionally, the same line can be represented in terms of any scalar multiple 'm' as:

Let's simplify:
therefore:
.
This matches the given line equation in choice (B).
Therefore correct options are choices (A) and (B).