Show that area of the parallelogram whose diagonals are given by `veca and vecb` is `|vecaxxvecb|/2` Also, find the area of the parallelogram whose diagonals are `2i -j+k and i +3j - k.`

Explanation

To solve the problem, we need to show that the area of the parallelogram whose diagonals are given by vectors \(\vec{a}\) and \(\vec{b}\) is \(\frac{|\vec{a} \times \vec{b}|}{2}\). Then, we will find the area of the parallelogram whose diagonals are \(2\vec{i} - \vec{j} + \vec{k}\) and \(\vec{i} + 3\vec{j} - \vec{k}\).

### Step 1: Show the Area of the Parallelogram
1. **Understanding the Diagonals**: Let \(\vec{a}\) and \(\vec{b}\) be the diagonals of the parallelogram. The diagonals bisect each other.
2. **Using Vectors**: Let the vectors representing the adjacent sides of the parallelogram be \(\vec{p}\) and \(\vec{q}\). The diagonals can be expressed as:
\[ \vec{a} = \vec{p} + \vec{q} \]
...