The dot product (or scalar product) is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors) and returns a single number.

Geometrically, it is the product of the Euclidean magnitudes of the two vectors and the cosine of the angle between them.

The Formula:

$$ A \cdot B = \sum_{i=1}^{n} A_i B_i = A_1B_1 + A_2B_2 + \dots + A_nB_n $$

Where $A = (A_1, A_2, \dots, A_n)$ and $B = (B_1, B_2, \dots, B_n)$.