Question

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

Answer 1

The answer is `=-50.9`

Explanation:

The dot product is `vecA.vecB`

`=〈3,1,-4〉.〈4,-7,3〉`

`=(3*4-1*7-4*3)`

`=12-7-12=-7`

The modulus of `vecA` is `=∥vecA∥=∥〈3,1,-4〉∥`

`=sqrt(9+1+16)=sqrt26`

The modulus of `vecB` is `=∥vecB∥=∥〈4,-7,3〉∥`

`=sqrt(16+49+9)=sqrt74`

Therefore,

`vecA.vecB-∥vecA∥*∥vecB∥`

`=-7-sqrt(26*74)`

`=-7-43.9=-50.9`