Question

What is the dot product of `<-8,5,2 >` and `<-3,1,7 >`?

Answer 1

`43`

Explanation:

For any 2 vectors `A=(a_1,a_2,...,a_n) and B=(b_1,b_2,...,b_n)` in a finite dimensional real or complex vector space X, the Euclidean inner product (dot product) is a real or complex number given by
`A*B=a_1b_1+a_2b_2+...+a_nb_n`.

So in this particular case, we work in `X=RR^3` and get

`(-8,5,2)*(-3,1,7)=(-8)(-3)+(5)(1)+(2)(7)`

`=24+5+14`

`=43` `inRR`.