# How do you find the inner product and state whether the vectors are perpendicular given #<-5,3>*<2,-3>#?

##### 1 Answer

Use the fact that the dot product of two vectors that are perpendicular is equal to zero.

#### Explanation:

The inner product (more commonly called the dot product) of two vectors of dimension n:

Is computed as follows:

The given vectors are of dimension 2:

Let

Let

Another way to compute the dot product is:

where:

and

If all that you care about is whether the vector are perpendicular, then you do not care about the magnitudes; you only care whether (or not) the dot product is zero.

If the two vectors were perpendicular, then

Because the dot product of the given vectors is NOT zero, one can say that the vectors are not perpendicular.