Question

what is the difference between difference between multiplication of vectors and vector product

Answer 1

multiplication of vectors maybe thier vector(cross) or scaler(dot) product,whereas vector product simply means that the resulting quantity between 2 vectors is another vector(having direction) unlike scaler which gives us no sense of direction.
EXAMPLE:
work(scaler)=force . displacement
torque(vector)=force x radius

Answer 2

Vector quantity needs both direction and magnitude to express them such as velocity acceleration etc and vector quantity can be taken product two ways as vector product or cross product and scalar product where in cross product is always another vector and in scalar product is always another scalar product.