What's the difference between the scalar product of a vector and the multiplication of two vectors? Generally speaking, what do two vectors OA · ob represent? For example, why is the multiplication of two vectors in the first question not equal to | OA · | ob | cos Sita?

What's the difference between the scalar product of a vector and the multiplication of two vectors? Generally speaking, what do two vectors OA · ob represent? For example, why is the multiplication of two vectors in the first question not equal to | OA · | ob | cos Sita?

The scalar product of a vector is the result of multiplication of two vectors. To be exact, it is the result of dot multiplication of two vectors. Just as the product is the result of multiplication of two numbers, what do you mean by it
There are two kinds of multiplication between vectors. In addition to the above-mentioned "dot product", there is another kind called "cross product". The result of cross product is called [vector product], also called outer product and cross product; and [scalar product] can be called correspondingly: inner product and dot product. If you have not learned vector product, you can equate vector multiplication with scalar product
As for this problem, as zddeng said, OA · OB and OA · ob · cos θ are equal. The latter is actually the definition of the former, they are only the difference of form. When you know the definition of quantity product, you can transform them at will
As a matter of fact, [OA · ob] is just a notation of vector product of quantity. In order to get the result, we must transform it according to the definition. [OA · ob · cos θ] is an idea, that is, to transform vector multiplication into multiplication of number and number. Another idea is [coordinate method]
For this problem, of course, the coordinate method is more convenient. Otherwise, you have to work out the length and angle of the vector according to the coordinates, and then use the length and angle to work out the scalar product, which is far away from the near