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Let vec(r)=(vec(a) times vec(b))sin x+(v...

Let `vec(r)=(vec(a) times vec(b))sin x+(vec(b) times vec(c))cosy+2(vec(c) times vec (a))` where `vec(a),vec(b),vec(c)` are non-zero and non-coplanar vectors. If `vec(r)` is orthogonal to `vec(a)+vec(b)+vec(c)`, then find the minimum value of `(20)/(pi^(2))(x^(2)+y^(2))`

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