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Given four vectors vec a,vec b, vec c, v...

Given four vectors `vec a,vec b, vec c, vec d` such that `vec a + vec b + vec c = alpha vec d , vec b +vec c + vec d = beta vec a` and that `vec a,vec b,vec c` are non-coplanar, then the sum `vec a +vec b + vec c + vec d` is

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