Question

If `A= <-5 ,-1 ,-3 >` and `B= <-6 ,-4 ,-7 >`, what is `A*B -||A|| ||B||`?

Answer 1

The answer is `=4.46`

Explanation:

The vectors are

`vecA= <-5,-1,-3>`

`vecB = <-6,-4,-7>`

The modulus of `vecA` is `=||vecA||=||<-5,-1,-3>||=sqrt((-5)^2+(-1)^2+(-3)^2)=sqrt(25+1+9)=sqrt35`

The modulus of `vecB` is `=||vecB||=||<-6,-4,-7>||=sqrt((-6)^2+(-4)^2+(-7)^2)=sqrt(36+16+49)=sqrt101`

Therefore,

`||vecA|| *||vecB||=sqrt35*sqrt101=sqrt3535`

The dot product is

`vecA.vecB= <-5,-1,-3> .<-6,-4,-7>`

`=(-5xx-6)+(-1xx-4)+(-3xx-7)`

`=30+4+21=55`

Therefore,

`vecA.vecB-||vecA|| xx||vecB||=55-sqrt3535= -4.46`