# 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.

#### 1 Comment

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

#### 1 Comment

Beulah A on 6 Nov 2019
Thanks, This solves my problem.

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