`A B C D` is a quadrilateral and `E` and the point intersection of the lines joining the middle points of opposite side. Show that the resultant of ` vec O A , vec O B , vec O Ca n d vec O D` is equal to 4 ` vec O E ,` where `O` is any point.

Explanation

To show that the resultant of the vectors \( \vec{OA}, \vec{OB}, \vec{OC}, \) and \( \vec{OD} \) is equal to \( 4 \vec{OE} \), where \( O \) is any point and \( E \) is the intersection of the lines joining the midpoints of opposite sides of the quadrilateral \( ABCD \), we can follow these steps:

### Step 1: Define the midpoints
Let \( P \) be the midpoint of side \( AB \) and \( Q \) be the midpoint of side \( CD \). By the definition of midpoints, we can express the vectors as:
\[ \vec{OP} = \frac{\vec{OA} + \vec{OB}}{2} \]
\[
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