# How to find angle between two lines?

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Beulah A on 21 Oct 2019
Commented: Beulah A on 6 Nov 2019
For example, there is line L1 between two points (x1,y1) and (x2,y2). Another line L2 between points (x1,y1) and (x3,y3). I want to find the angle between the lines L1, L2. How to find in MATLAB? I think in matlab there is no predefined function which performs the same.
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James Tursa on 21 Oct 2019

Bjorn Gustavsson on 21 Oct 2019
A more stable method that what Jos suggested is
v_1 = [x2,y2,0] - [x1,y1,0];
v_2 = [x3,y3,0] - [x1,y1,0];
Theta = atan2(norm(cross(v_1, v_2)), dot(v_1, v_2));
HTH
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Beulah A on 6 Nov 2019
Thanks, This solves my problem.

### More Answers (2)

Jos (10584) on 21 Oct 2019
Use the dot product between the two vectors (v1 and v2) given by the four x,y pairs points.
Given the formula: dot(v1,v2) = | v1 | x | v2 | x cos(A)
I leave it to you to find the angle A using the matlab functions norm, dot and acos.

Bjorn Gustavsson on 21 Oct 2019