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

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Answer 1 · 2017-01-29T12:17:15

$16 - sqrt 53 - sqrt 65$

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

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

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

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

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

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