Question

If `A= <2 -5 >` and `B= <9, 4 >`, what is `||A+B|| -||A|| -||B||`?

Answer 1

The answer is `=sqrt122-sqrt29-sqrt97=-4.2`

Explanation:

`vecA=〈2,-5〉`

`vecB=〈9,4〉`

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

`vecA+vecB=〈2,-5〉+〈9,4〉=〈11,-1〉`

The modulus of `vecA=∥〈2,-5〉∥=sqrt(4+25)=sqrt29`

The modulus of `vecB=∥〈9,4〉∥=sqrt(81+16)=sqrt97`

The modulus of `vecA+vecB=∥〈11,-1〉∥=sqrt(121+1)=sqrt122`

So, `∥vecA+vecB∥-∥vecA∥-∥vecB∥=sqrt122-sqrt29-sqrt97`

`=-4.2`