Does the dot product or the scalar product's general formula will be A.B=AB cos theta? or as long as the vectors are parallel it can change into sin theta?

Scalar product is also called dot product is |A| |B| cos theta

If A and B are parallel then cos theta = 1 and you have |A| |B|

The VECTOR product is also called Cross product has magnitude of |A| |B| sin theta and is a vector perpendicular to both A and to B (like up is perpendicular to North and Northeast)