Angle Between two vectors.

How could I create a function that will take two vectors as inputs, and outputs the angle between them in radians.

Answer 1

[Jim Riggs]

Given two vectors A and B, the dot product of the two vectors (A dot B) gives the product ABcos(ang), so to get just the angle, you want to take the dot product of two unit vectors;

Assume A = [ax, ay, az], B = [bx, by, bz]

magA = sqrt(ax^2+ay^2+az^2);  % = sqrt(A(1)^2 + A(2)^2 + A(3)^2)
magB = sqrt(bx^2+by^2+bz^2);  % = sqrt(B(1)^2 + B(2)^2 + B(3)^2)
UA = [ax/magA, ay/magA, az/magA];  % A unit vector,  = [A(1)/magA, A(2)/magA, A(3)/magA]
UB = [bx/magB, by/magB, bz/magB];  % B unit vector,  = [B(1)/magB, B(2)/magB, B(3)/magB]
cosAng = dot(UA,UB);  % = UA(1)*UB(1) + UA(2)*UB(2) + UA(3)*UB(3) 
ang = acos(cosang);  % This is the angle between vector A and Vector B, in radians

As a function;

function ang = Vangle(A,B)
    magA = sqrt(A(1)^2 + A(2)^2 + A(3)^2);
    magB = sqrt(B(1)^2 + B(2)^2 + B(3)^2);
    UA = [A(1)/magA, A(2)/magA, A(3)/magA]
    UB = [B(1)/magB, B(2)/magB, B(3)/magB]
    cosAng =  UA(1)*UB(1) + UA(2)*UB(2) + UA(3)*UB(3); 
    ang = acos(cosang); 
    return 
end

[Andrew Bass]

thank you! this was very helpful

Answer 2

[James Tursa]

This has been discussed many times on this forum. Robust methods are found here:

https://www.mathworks.com/matlabcentral/answers/101590-how-can-i-determine-the-angle-between-two-vectors-in-matlab

And a full circle method can be found here:

https://www.mathworks.com/matlabcentral/answers/501449-angle-betwen-two-3d-vectors-in-the-range-0-360-degree