The postion vectors of the vertrices fo aquadrilateral with A as origian are `B(vecb),D(vecd) and C (l vecb+m vecd)` . Prove that the area of the quadrilateral is `1/2(l+m)|vecb xx vecd|`.

Explanation

To prove that the area of the quadrilateral formed by the position vectors of the vertices A (origin), B (vector b), D (vector d), and C (l vector b + m vector d) is given by \( \frac{1}{2}(l+m)|\vec{b} \times \vec{d}| \), we can follow these steps:

### Step 1: Identify the position vectors
Let the position vectors of the points be:
- \( \vec{A} = \vec{0} \) (origin)
- \( \vec{B} = \vec{b} \)
- \( \vec{D} = \vec{d} \)
- \( \vec{C} = l\vec{b} + m\vec{d} \)
...