Scalar product of vectors online calculator

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

ababcosφ

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

Commutativity:

abba

Associativity, relative to scalar multiplier (α):

associativity feature of the scalar product

Distributivity:

cabcacb

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:

abaxbxaybyazbz

, where and .

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

Vectors scalar product calculator
Vector A by:
Vector B by:
ab12543
Vector A = { }
Vector B = { }


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