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(b)` . Then find the value of `|vec(a)+vec(b)+vec(c)|` .

Answer

`=>|vec(a)+vec(b)+vec(c)|=5sqrt(2)`