Finding a 3D parallel vector

Hello,

I am looking for a unit vector that starts at a point (l,m,n) and it's, at the same time, parallel to the line that goes from (a,b,c) to (d,e,f). Can anyone help me with this problem?

Thank you, AF.

Answer 1

[James Tursa]

A unit vector parallel to the points from (a,b,c) to (d,e,f) is just this:

v1 = [a,b,c];
v2 = [d,e,f];
u = v2 - v1;
u = u/norm(u);

A point on a parallel line that goes through (l,m,n) is then just this:

p = [l,m,n];
x = any scalar value
point_on_line = p + x * u;

[Alonso Figueroa]

Great, thank you James!