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Let vec a , vec b , and vec c are vecto...

Let ` vec a , vec b , and vec c` are vectors such that `| vec a|=3,| vec b|=4 and | vec c|=5, and ( vec a+ vec b)` is perpendicular to ` vec c ,( vec b+ vec c)` is perpendicular to ` vec a and ( vec c+ vec a)` is perpendicular to ` vec bdot` Then find the value of `| vec a+ vec b+ vec c|` .

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