If

vector A = {x1, y1, z1}
vector B = {x2, y2, z2}

then

angle = arccos (((x1 * x2) + (y1 * y2) + (z1 + z2))/(((x1^2 + y1^2 + z1^2)*(x2^2 + y2^2 + z2^2))^(1/2)))