Question

If `A= <7 , 2>` and `B= <8, -1 >`, what is `||A+B|| -||A|| -||B||`?

Answer 1

`16 - sqrt 53 - sqrt 65`

Explanation:

The formula is Pythagorean and Euclidean
`mod(x, y) = sqrt{x^2 + y^2}`

The distance from `(x, y)` to `(0, 0)`.

`mod(7, 2) = sqrt{49 + 4} = sqrt 53`

`mod(8, -1) = sqrt {64 + 1} = sqrt 65`

`mod (7 + 8, 2 - 1) = sqrt{225 + 1} = 16`