Only the Sum and the Difference Survived

A delivery drone flies exactly two legs, described by vectors $\vec{A}$ and $\vec{B}$ . Its flight recorder has a bug: instead of storing the legs themselves, it stored only their sum and their difference.

$\vec{A} + \vec{B} = (7,\ 1) \qquad\quad \vec{A} - \vec{B} = (1,\ 9)$

What is the magnitude of the second leg, $\|\vec{B}\|$ ?

Only the Sum and the Difference Survived

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