Question

If `A= <-1 ,1 ,-4 >` and `B= <3 ,2 ,4 >`, what is `A*B -||A|| ||B||`?

Answer 1

`(-17)-3sqrt58`

Explanation:

`(x1,y1,z1)*(x2,y2,z2)=x1x2+y1y2+z1z2`

`(-1,1,-4)*(3,2,4)=(-3)+2-16=-17`

`absA` means the distance from point A to 0(0,0,0)

`absA=sqrt((-1)^2+1^2+(-4)^2`
=`3sqrt2`

`absB=sqrt(3^2+2^2+4^2`
=`sqrt29`

so `A*B-absAabsB`
`=(-17)-3sqrt2*sqrt29`
`=(-17)-3sqrt58`