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If D,E and F are the mid-points of the s...

If D,E and F are the mid-points of the sides BC,CA and AB, respectively of a `DeltaABC` and O is any point, show that
(i) AD+BE+CF=0
(ii) OE+OF+DO=OA

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AI Generated Solution

To solve the problem step by step, we will break it down into two parts as stated in the question. ### Part (i): Show that \( AD + BE + CF = 0 \) 1. **Define the position vectors**: Let the position vectors of points \( A \), \( B \), and \( C \) be represented as \( \vec{a} \), \( \vec{b} \), and \( \vec{c} \) respectively. 2. **Find the midpoints**: ...
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