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Question

If $a = 3$, $b = 4$, and $c = 5$, each one of $\vec{a}$, $\vec{b}$, and $\vec{c}$ is perpendicular to the sum of the remaining vectors. Then, $|\vec{a} + \vec{b} + \vec{c}|$ is equal to

$\frac{5}{\sqrt{2}}$

$\frac{2}{\sqrt{5}}$

$5\sqrt{2}$

$\sqrt{5}$

Solution

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