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:
Associativity, relative to scalar multiplier (α):
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
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