A,B,C,D are four points in the space and satisfy ∣vec(AB)∣=3,∣vec(BC)∣=7,∣vec(CD)∣=11 and ∣vec(DA)∣=9. Then vec(AC).vec(BD) is I know that vec(AB)+vec(BC)+vec(CA)+vec(AD)=0 and also I observed that ∣vec(AB)∣^2+∣vec(CD)∣^2=∣vec(BC)∣^2+∣vec(DA)∣^2. But couldn't get anything from it. Any hint?

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