Question

How would I use the dot product of `u` if `u``=``5i``+``2j`?

Answer 1

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 `v=4i+3j` be another 2 dimensional vector.

Then the dot product of `u` with `v` is

`u*v=(5i+2j)*(4i+3j)`

`=(5xx4)+(2xx3)`

`=26`.

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

`u*u=||u||^2=(sqrt(5^2+2^2))^2=(sqrt29)^2=29`.

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. `W=F*x`.
The magnitude hereof may then be evaluated as `Fxcostheta` where `theta` is the angle between `F and x`.