Question

If `A= <8 ,-5 ,9>` and `B= <5 ,4 ,-9 >`, what is `A*B -||A|| ||B||`?

Answer 1

The answe is `=-205`

Explanation:

The dot product of 2 vectors
`vecA.vecB=〈A_1,A_2,A_3〉.〈B_1,B_2,B_3〉`
`=A_1B_+A_2B_2+A_3B_3`
So here we have
`〈8,-5,9〉.〈5,4,-9〉=40-20-81=-61`
`∣〈A_1,A_2,A_3〉∣=sqrt(A_1^2+A_2^2+A_3^2)`
`=sqrt(64+25+81)=sqrt170`
`∣〈B_1,B_2,B_3〉∣=sqrt(B_1^2+B_2^2+B_3^2)`
`=sqrt(25+16+81)=sqrt122`
And finally, we have
`vecA.vecB-∣vecA∣∣vecB∣=-61-sqrt(170*122)=-61-144=-205`