Scalar product of the vectors is the product of their magnitudes (lengths) and cosine of angle between them:

The above formula reads as follows: the scalar product of the vectors is scalar (number). In addition, scalar product holds the following features:

Commutativity:

Associativity, relative to scalar multiplier (α):

Distributivity:

Two non-zero vectors are perpendicular if and only if their scalar product equals to zero:

In the coordinate form, scalar product of two vectors is expressed by the formula:

, where and .

Our online calculator is able to find scalar product of two vectors with step by step solution.

Vectors scalar product calculator

by:

by:

= { }

= { }

Install calculator on your site