Question

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

Answer 1

The answer is `=sqrt116-sqrt37-sqrt41=-1.72`

Explanation:

`vecA=〈6,-1〉`

`vecB=〈4,5〉`

`vecA+vecB=〈6,-1〉+〈4,5〉=〈10,4〉`

The modulus of `vecA+vecB=∥〈10,4〉∥=sqrt(100+16)=sqrt116`

The modulus of `vecA=∥〈6,-1〉∥=sqrt(36+1)=sqrt37`

The modulus of `vecB=∥〈4,5〉∥=sqrt(16+25)=sqrt41`

Therefore,

`∥vecA+vecB∥-∥vecA∥-∥vecB∥=sqrt116-sqrt37-sqrt41`

`=-1.72`