Question

If `A= <2 ,1 ,-4 >` and `B= <3 ,2 ,-5 >`, what is `A*B -||A|| ||B||`?

Answer 1

The answer is `=-0.25`

Explanation:

Here we need the dot product and the modulus

The dot product is `=〈a,b,c〉.〈d,e,f〉=ad+be+cf`

The modulus of a vector is `=∥〈a,b,c〉∥=sqrt(a^2+b^2+c^2)`

Here we have `vecA=〈2,1,-4〉` and `vecB=〈3,2,-5〉`

`vecA.vecB=〈2,1,-4〉.〈3,2,-5〉=6+2+20=28`

The modulus of `vecA`

`=∥〈2,1,-4〉∥=sqrt(4+1+16)=sqrt21`

The modulus of `vecB`

`=∥〈3,2,-5〉∥=sqrt(9+4+25)=sqrt38`

Therefore,

`vecA.vecB-∥vecA∥∥vecB∥=28-sqrt21sqrt38`

`=28-sqrt798=28-28.25=-0.25`