Question

If `A= <-2 ,-7 ,-1 >` and `B= <3 ,4 ,-8 >`, what is `A*B -||A|| ||B||`?

Answer 1

The answer is `=-95.3`

Explanation:

The vectors are

`vecA= <-2,-7,-1>`

`vecB = <3,4,-8>`

The modulus of `vecA` is `=||vecA||=||<-2,-7,-1>||=sqrt((-2)^2+(-7)^2+(-1)^2)=sqrt(4+49+1)=sqrt54`

The modulus of `vecB` is `=||vecB||=||<3,4,-8>||=sqrt((3)^2+(4)^2+(-8)^2)=sqrt(9+16+64)=sqrt89`

Therefore,

`||vecA|| xx||vecB||=sqrt(54)*sqrt89=sqrt4806`

The dot product is

`vecA.vecB= <-2,-7,-1> .<3,4,-8> =(-2xx3)+(-7xx4)+(-1xx-8)=-6-28+8=-26`

Therefore,

`vecA.vecB-||vecA|| xx||vecB||=-26-sqrt4806= -95.3`