Prove that the area of a parallelogram with sides `vec(A) and vec(B) " is " vec(A) xx vec(B)`

Explanation

To prove that the area of a parallelogram with sides \(\vec{A}\) and \(\vec{B}\) is given by \(\vec{A} \times \vec{B}\), we can follow these steps:

### Step 1: Understand the Geometry of the Parallelogram
Consider a parallelogram with two adjacent sides represented by vectors \(\vec{A}\) and \(\vec{B}\). The angle between these two vectors is denoted as \(\theta\).

### Step 2: Identify the Base and Height
In a parallelogram, the area can be calculated using the formula:
\[
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