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Let vec(a) , vec(b) and vec(c) be three ...

Let `vec(a) , vec(b)` and `vec(c)` be three vectors of magnitudes 3, 4 and 5, respectively. If each one is perpendicular to the sum of the other two vectors, then prove that `|vec(a) + vec(b) + vec(c)| = 5sqrt(2)`.

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The correct Answer is:
`5sqrt(2)`
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