@elijah

I know that for a line to be parallel , the vector ( dir ) of the line must be the same. I have a line in 3d and I need to create another parallel line above and below the existing line at a given offset. Can anybody help me or give me some idea on how to accomplish this. I thought of just adding so offset value for the given axis on the the origin of the line. But I do not know whether this is correct?

It’s not possible. Think abou it: what does “above” or “below” mean given we have three dimensions? You need just one more primitive (i.e. point) to fix a plane and then you can place additional lines. Non-zero offset of both the points will indeed result in a parallel line, although the concept of below or above will still not exist.

I know that for a line to be parallel , the vector ( dir ) of the line must be the same. I have a line in 3d and I need to create another parallel line above and below the existing line at a given offset. Can anybody help me or give me some idea on how to accomplish this. I thought of just adding so offset value for the given axis on the the origin of the line. But I do not know whether this is correct?