If $|\vec{a}| = 3, |\vec{b}| = 4$ and $|\vec{a} + \vec{b}| = 5$, then $|\vec{a} - \vec{b}| =$

5

The correct answer is Option (3) → 5 ##

$|\vec{a}| = 3, |\vec{b}| = 4, |\vec{a} + \vec{b}| = 5$

We have, $|\vec{a} + \vec{b}|^2 + |\vec{a} - \vec{b}|^2 = 2(|\vec{a}|^2 + |\vec{b}|^2)$

$= 2(9 + 16) = 50\Rightarrow |\vec{a} - \vec{b}|^2 = 50 - 5^2 = 25 \Rightarrow |\vec{a} - \vec{b}| = 5$