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Figure shows a parallelogram ABCD. Prove...

Figure shows a parallelogram ABCD. Prove that `vec(AC)+ vec (BD) = 2 vec(BC)`'

Text Solution

Verified by Experts

The correct Answer is:
`2vec(BC)`
`vec(AC)=vec(AB)+vec(BC)`
`vec(BD)=vec(BC)+vec(CD)` [applying triangle law of vectors]
Now `vec(AC)+vec(BD)=vec(AB)+vec(BC)+vec(BC)+vec(CD)=vec(AB)+2vec(BC)+vec(CD)`
But `vec(CD)=-vec(AB) therefore vec(AC)+vec(BD)=vec(AB)+2vec(BC)-vec(AB)=2vec(BC)`
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