Question

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

Answer 1

The answer is `=-92.7`

Explanation:

`vecA=〈-1,6,-4〉`

`vecB=〈3,-5,3〉`

The dot product is `vecA.vecB=〈-1,6,-4〉.〈3,-5,3〉`

`=-3-30-12=-45`

The modulus of `vecA` is `=∥vecA∥=∥〈-1,6,-4〉∥`

`=sqrt(1+36+16)=sqrt53`

The modulus of `vecB` is `=∥vecB∥=∥〈3,-5,3〉∥`

`=sqrt(9+25+9)=sqrt43`

Therefore,

`vecA.vecB-∥vecA∥*∥vecB∥=-45-sqrt53*sqrt43`

`=-45-47.7=-92.7`