why we take sin in cross product & cos in dot product?
Definition of cross product says that it is another vector, that is perpendicular to each of given vectors and this 3 vectors have right
orientation, and length of third vector is equal product of lengths of first two vectors and sine of angle between them. Other words length of vector cross-product is area of parallelogram built on given 2 vectors. Since area of parallelogram includes sine in its formula, then we take sine.
In dot product we take projection& of the first vector on another one, and that is why we used cosine.