In words, the scalar product of two vectors can be thought of as the product of the magnitude of ~a with the magnitude of the projection of ~b onto the direction of ~a. it is used to calculate the product of vector quantities when only the parallel components of each vector contribute (e. g., work = force • displacement). let ~a = h9, 6.75, 0i and ~b = h2.97, 6.075, 0i. calculate ~a • ~b.