Question

If `A= <2 ,6 ,-3 >` and `B= <-6 ,2 ,7 >`, what is `A*B -||A|| ||B||`?

Answer 1

The answer is `=-21-7sqrt89`

Explanation:

The dot product `vecA.vecB=〈2,6,-3〉.〈-6,2,7〉`
`=2*-6+6*2+7*-3=-12+12-21=-21`
The modulus of `vecA` , `=∥vecA∥=∥〈2,6,-3〉∥=sqrt(4+36+9)`
`=sqrt49=7`
The modulus of `vecB` , `=∥vecB∥=∥〈-6,2,7〉∥=sqrt(36+4+49)`
`=sqrt89`
And finally we have `(vecA.vecB-∥vecA∥*∥vecB∥)=-21-7sqrt89`