How do you find the inner product and state whether the vectors are perpendicular given #<8,4>*<2,4>#?
The inner product gives
The inner product of two vector (of equal length, of course), is simply given by the sum of the products of the coordinates with same index.
In generale, if you have two vectors
Furthermore, two vectors are said to be perpendicular if their inner product is zero, i.e.
In your case, the inner product is
and so the vectors are not perpendicular.
Note: if your change the sign of any of the four coordinates, they actually become perpendicular: for example,