Question

If `A= <6 ,9 ,-1 >` and `B= <-4 ,-9 ,4 >`, what is `A*B -||A|| ||B||`?

Answer 1

`A*B-||A|| ||B||=-224,47`

Explanation:

`A= <6,9,-1>" "B= <-4,-9,4>`
`A= < a,b,c >" "B= < d,e,f >`
`A*B=a*d+b*e+c*f`
`A*B=-24-81-4=-109`
`||A||=sqrt(a^2+b^2+c^2)" "||A||=sqrt(36+81+1)=sqrt118`
`||B||=sqrt(d^2+e^2+f^2)" "||B||=sqrt(16+81+16)=sqrt113`
`A*B-||A|| ||B||=-109-(sqrt118*sqrt113)`
`A*B-||A|| ||B||=-109-sqrt(118*113)`
`A*B-||A|| ||B||=-109-115,47`
`A*B-||A|| ||B||=-224,47`