Finding a 3D parallel vector

2018 7 24
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更新时间：2018 7 25
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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.

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James Tursa
James Tursa 2018-7-24
编辑：James Tursa 2018-7-24

2 个投票

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;

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