If `veca, vecb and vecc` are vectors such that `|veca|=3,|vecb|=4 and |vecc|=5 and (veca+vecb)` is perpendicular to `vecc,(vecb+vecc)` is perpendicular to `veca` and `(vecc+veca)` is perpendicular to `vecb` then `|veca+vecb+vecc|=` (A) `4sqrt(3)` (B) `5sqrt(2)` (C) 2 (D) 12

Explanation

To solve the problem, we need to find the magnitude of the vector sum \( \vec{a} + \vec{b} + \vec{c} \) given the conditions about their magnitudes and the perpendicular relationships. Let's break it down step by step.

### Step 1: Understand the given information
We have three vectors:
- \( |\vec{a}| = 3 \)
- \( |\vec{b}| = 4 \)
- \( |\vec{c}| = 5 \)

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