Question

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

Answer 1

The answer is `sqrt34-sqrt37-sqrt45`

Explanation:

The modulus of a vector `〈x,y〉` is `=sqrt(x^2+y^2)`

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

So modulus of `vecB` is `∥〈-3,6〉∥=sqrt(9+36)=sqrt45`

`〈vecA〉+〈vecB〉 =〈6,-1〉+〈-3,6〉=〈3,5〉`

So the modulus of `〈vecA〉+〈vecB〉` is`∥〈vecA〉+〈vecB〉∥`

`=sqrt(9+25)=sqrt34`

And finally
`∥vecA+vecB∥-∥vecA∥-∥vecB∥ =sqrt34-sqrt37-sqrt45`