The scalar product of two vectors and is given in terms of their scalar components (a_x,a_y) and (b_x,b_y) by the expression

= a_xb_x + a_yb_y .

This expression assumes that the vectors are two-dimensional. In three dimensions, a third term a_zb_z needs to be added.

The value is a scalar that depends only on the two vectors involved, and not on the coordinate system used to define their components.

You can verify this by rotating the coordinate axes and thus changing the components. To rotate the axes, click on the positive end of either axis and drag it. Then recalculate the value of the scalar product with the new components and check that the value has not changed.