For two vectors `vec(A)` and `vec(B)` if `vec(A) + vec(B) = vec(C)` and `A +B = C`, then prove

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For two vectors `vec(A)` and `vec(B)` if `vec(A) + vec(B) = vec(C)` and `A +B = C`, then prove that `vec(A)` and `vec(B)` are parallel to each other.

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