Scalar Product of Two Vectors
The scalar product (or dot product) of two vectors is defined as the product of the magnitudes of both the vectors and the cosine of the angle between them.
Thus if there are two vectors and having an angle θ between them, then their scalar product is defined as ⋅ = AB cos θ. Here, A and B are magnitudes of and .
The product quantity ⋅ is always a scalar. It is positive if the angle between the vectors is acute (i.e., < 90°) and negative if the angle between them is obtuse (i.e. 90°<θ< 180°).
The work done is basically a scalar product between the force vector and the displacement vector. Apart from work done, there are other physical quantities which are also defined through scalar products.