I have two vectors

A = 2i + 3j + 4k

B = 5i + 6j + 7k

I wish to find out the angle between them with the proper sign.

I read (Maths - Inverse Trigonometric Functions - Martin Baker) that the function atan2 is the right way to do it. But I don't find the method to go about it. I want to do it by hand not using some software or excel or something.

Anyone throw some light on it or any other proper method.