Question

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

Answer 1

The dot (scalar) product `A*B=28`. The length of vector A, `||A||=`, and the length of vector B, `||B||=`. Over all, `A*B-||A||||B||=28-80.84=-52.84` `units`.

Explanation:

The question is essentially 'What is the difference between the dot product of two vectors and the product of their lengths?'

First find the dot product:

`A*B = ((-8*-3)+(3*4)+(-1*8)`
`= (24+12-8)=28` `units`

Now the length of each vector:

`||A||=sqrt((-8)^2+3^2+(-1)^2)=sqrt(64+9+1)=sqrt74~~8.6`

`||B||=sqrt((-3)^2+4^2+8^2)=sqrt(9+16+64)=sqrt89~~9.4`

So the product `||A||||B||=8.6xx9.4=80.84`