Mathematics

Problem

|\vec{a}| = 3

|\vec{b}| = 4

|\vec{c}| = 5

such that each is perpendicular to sum of the other two, then

|\vec{a} + \vec{b} + \vec{c}| =

(A)

5\sqrt{2}

(B)

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

(C)

10\sqrt{2}

(D)

5\sqrt{3}