Scalar product of vectors online calculator

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

defenition of the scalar product of the vectors

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

Commutativity:

commutativity feature of the scalar product

Associativity, relative to scalar multiplier (α):

associativity feature of the scalar product

Distributivity:

distributivity feature of the scalar product

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

perpendicular condition of the scalar product

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

formula for scalar product calculation

vectors coordinates

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

Input vectors dimension

Vectors dimension
Vector vector A representations form:
Vector vector B representation form:
Vector vector A = { }
Vector vector A:
Vector vector B = { }
Vector vector B: