Why A .A =||A||^2(dot product) in vector analysis. Every where in vector analysis mathematicians used this result. To prove A.B = ||A|| ||B||cos(theta) we assume that A.A is ||A||^2 , without assuming this we can't prove A.B = ||A|| ||B||cos(theta) . I think they assumed it because dot product is approximately a multiplication of magnitude (only for A.A because both vectors have same direction therefore it will not effect the direction of resultant and in dot product we don't need direction, therefore we simply write A.A= ||A||^2) I want to know your opinion on this, is there a good reason for this. And please do not say that A.A = ||A||^2 because cos(theta) =1 in this case.