Let `vec(A),vec(B),vec(C )` be vectors of length 3, 4, 5, respectively Let `overset(to)(A)` be perpendicular to `overset(to)(B) +overset(to)(C ) , overset(to)(B) " to " overset(to)( C) + overset(to)(A) " and " overset(to)(C )` to `overset(to)(A) +overset(to)(B)` then the length of vector `overset(to)(A) +overset(to)(B)+overset(to)(C )` is .......