distance between two parallel lines in 3D

[BigAl]

So I have to find a formula for the distance between two parallel lines. Since the distance between these lines is always constant, is the distance just the magnitude of the normal vector? I'm a bit confused.

Edit: I dont think the normal vector exists between two parallel lines.

[brightsky]

let the two parallel lines be l1 and l2. take a random point P on l1. find the direction vector b of l2. now all we need to do is find the shortest distance between a point and a line, which can be done in one of two ways:

1. let Q be a generic point on l2, expressed in terms of parameter t. solve PQ.b = 0 to find the value of t for which PQ is perpendicular to l2. now find the norm of PQ.

2. let A be a random point on l2. find the scalar resolute of AP perpendicular to b.

[BigAl]

let the two parallel lines be l1 and l2. take a random point P on l1. find the direction vector b of l2. now all we need to do is find the shortest distance between a point and a line, which can be done in one of two ways:

1. let Q be a generic point on l2, expressed in terms of parameter t. solve PQ.b = 0 to find the value of t for which PQ is perpendicular to l2. now find the norm of PQ.

2. let A be a random point on l2. find the scalar resolute of AP perpendicular to b.

Yes that makes sense now. thanks