How do you find the inner product and state whether the vectors are perpendicular given #<-5,3>*<2,-3>#?
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:
Another way to compute the dot product is:
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.