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Mathematical Expression Editor
Dot Product and its Properties
Let and be vectors in . The dot product of and , denoted by , is given by
Find if and .
Note that the dot product of two vectors is a scalar. For this reason, the dot product
is sometimes called a scalar product.
Properties of the Dot Product
A quick examination of Example ex:dotex will convince you that the dot product is
commutative. In other words, . This and other properties of the dot product are
stated below.
The following properties hold for vectors , and in and scalar in .
(a)
(b)
(c)
(d)
(e)
, and if and only if .
(f)
We will prove Property item:distributive. The remaining properties are left as exercises.