Scalar Product

The Scalar Product is an operation that converts two (or more) vectors into a scalar.

{I’m a bit cautious on the ‘or more’ part. To me, it seems that once the two vectors are converted to a scalar, nothing more can be done, other than using that to scale something else.}

\overrightarrow a \cdot \overrightarrow b = ab cos \: \theta

I also found it written this way:

\overrightarrow a \cdot \overrightarrow b = |a||b| cos \: \theta

|b|cosθ is the projection of the vector b on the vector a.

Scalar Products are commutative:

a \cdot b = b \cdot a

The Scalar Product follows the distributive law (multiplication distributes over addition):

a \cdot (b + c) = a \cdot b + a \cdot c