According to the definition of vector product (also called quantity product), the product of two vectors is equal to the product of the amplitude of each vector and the cosine of the included angle between the two vectors. See the figure below:

Vector OA* vector ob = r1* R2 * cos θ = r1* R2 * cos (α-β) = r1* R2 * (cos α cos β+sin α sin β).

= r1cos α * r2cos β+r1sin α * r2sin β = x1* x2+y1* y2, that is, the vector multiplication is equal to the sum of the horizontal and vertical multiplication respectively. I hope I can help you!