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

Explanation

To solve the problem, we need to show two statements involving the midpoints of the sides of triangle ABC and a point O. Let's denote the position vectors of points A, B, C, D, E, F, and O as follows:

- Let the position vector of point A be \(\vec{a}\)
- Let the position vector of point B be \(\vec{b}\)
- Let the position vector of point C be \(\vec{c}\)
- Let the position vector of point D (midpoint of BC) be \(\vec{d} = \frac{\vec{b} + \vec{c}}{2}\)
- Let the position vector of point E (midpoint of CA) be \(\vec{e} = \frac{\vec{c} + \vec{a}}{2}\)
- Let the position vector of point F (midpoint of AB) be \(\vec{f} = \frac{\vec{a} + \vec{b}}{2}\)
...