`A B C D` is a quadrilateral. `E` is the point of intersection of the line joining the midpoints of the opposite sides. If `O` is any point and ` vec O A+ vec O B+ vec O C+ vec O D=x vec O E ,t h e nx` is equal to a. `3` b. `9` c. `7` d. `4`

Options

A. 3
B. 9
C. 7
D. 4

Explanation

To solve the problem, we need to find the value of \( x \) in the equation \( \vec{OA} + \vec{OB} + \vec{OC} + \vec{OD} = x \vec{OE} \), where \( E \) is the point of intersection of the lines joining the midpoints of the opposite sides of quadrilateral \( ABCD \).

### Step-by-Step Solution:

1. **Define Position Vectors**:
Let:
\[
\vec{OA} = \vec{a}, \quad \vec{OB} = \vec{b}, \quad \vec{OC} = \vec{c}, \quad \vec{OD} = \vec{d}
...