Angle between two vectors matlab

Question

I want to calculate the angle between 2 vectors V = [Vx Vy Vz] and B = [Bx By Bz]. is this formula correct?

VdotB = (Vx*Bx + Vy*By         


        

Answer 1

There are a lot of options:

a1 = atan2(norm(cross(v1,v2)), dot(v1,v2))
a2 = acos(dot(v1, v2) / (norm(v1) * norm(v2)))
a3 = acos(dot(v1 / norm(v1), v2 / norm(v2)))
a4 = subspace(v1,v2)

All formulas from this mathworks thread. It is said that a3 is the most stable, but I don't know why.

For multiple vectors stored on the columns of a matrix, one can calculate the angles using this code:

% Calculate the angle between V (d,N) and v1 (d,1)
% d = dimensions. N = number of vectors
% atan2(norm(cross(V,v2)), dot(V,v2))
c = bsxfun(@cross,V,v2);
d = sum(bsxfun(@times,V,v2),1);%dot
angles = atan2(sqrt(sum(c.^2,1)),d)*180/pi;