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If \( \vec{a}, \vec{b} \) and \( \vec{c} \) are three vectors such that
\( \mathrm{P} \)
W \( |\vec{a}|=3,|\vec{b}|=4 \) and \( |\vec{c}|=\sqrt{24} \) and sum of any two vectors is orthogonal to third vector, then \( |\vec{a}+\vec{b}+\vec{c}| \) is equal to
(1) 7
(2) \( 5 \sqrt{2} \)
(3) \( 7 \sqrt{2} \)
(4) \( 6 \sqrt{2} \)
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