How would I use the dot product of #u# if #u##=##5i##+##2j#?
1 Answer
The dot product (also called Euclidean inner product) of any 2 n-dimensional vectors is a scalar real or complex numbers.
So the dot product is an operator which operates on 2 vectors to produce a real or complex number.
Hence you cannot have the dot product of just 1 vector.
For example, let
Then the dot product of
Note that we may take the dot product of a vector with itself (not sure if that is what you meant to ask), and in that case we get it equal to the norm of the vector squared, that is
The dot product has many uses and applications in everyday life.
For example, in mechanics we define work to be the dot product between the resultant force and the displacement.
The magnitude hereof may then be evaluated as