# Scalar product of vectors online calculator

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

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

Commutativity:

Associativity, relative to scalar multiplier (α):

Distributivity:

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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:

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

## Input vectors dimension

Vectors dimension
2
3

Vector
representations form:
coordinates
points

Vector
representation form:
coordinates
points

Vector
= { }

Vector
:

Vector
= { }

Vector
: