Question

Two vectors u and v are given `u=5i-9j-9k, v=4/5i+4/3j-k`, how do you find their dot product?

Answer 1

The answer is `=1`

Explanation:

If we have 2 vectors `vecA=〈a,b,c〉`

and `vecB=〈d,e,f〉`

The dot product is

`vecA.vecB=〈a,b,c〉.〈d,e,f〉=ad+be+cf`

Here. `vecu=〈5,-9,-9〉` and

`vecv=〈4/5,4/3,-1〉`

The dot product is

`vecu.vecv=〈5,-9,-9〉.〈4/5,4/3,-1〉`

`=5*4/5-9*4/3+(-9*-1)`

`=4-12+9=1`