Question

Consider the following vectors: v = 3i + 4j, w = 4i + 3j, how do you find the dot product v·w?

Answer 1

`24`

Explanation:

Definition : Let `v = (v_1,v_2,....,v_n) and w=(w_1,w_2,...,w_n)` be any 2 vectors in `RR^n or CC^n`.
Then the Euclidean inner product (also called dot product) of `v` with `w`is a real or complex number defined by
`v*w=v_1w_1+v_2w_2+.....+v_nw_n`.

So in this particular case we work in `RR^2` and get,

`(3,4)*(4,3)=(3xx4)+(4xx3)=12+12=24in RR`.