The dot product is an algebraic operation that takes 2 equally sized vectors and returns a single scalar number. The dot product is usually denoted with a symbol.

The dot product can be defined as follows:

Where is the size of the vectors.

The dot product can also be defined geometrically in 2 dimensions as follows

where is the angle between the two vectors

Properties

Two vectors are orthogonal if their dot product is 0. This is evident from the term in the 2d geometric interpretation.