
Calculate the scalar product of two vectors 
The multiplication of vectors has been briefly described in the section Vectors Calculation. It was shown that the result is not a vector but a real number (scalar product or dot product).
This section describes the calculation of the scalar product; and how the angle between the vectors can be calculated with the help of the scalar product.

For the two vectors and the scalar produkt is defined as 
Example: 


Calculate angle between two vectors 
From the scalar product described above and the magnitude of the vectors, the angle included by the vectors can be calculated.

The following formula is used for this: 
The following example calculates the angle of the vectors 

The result is : 
The figure below shows the graphical representation of the vectors and the angle 


