Determine the area of a parallelogram whose diagonals are given by vectors `3hati+2hatj-7hatk and 5hati+6hatj-3hatk` .

Explanation

To determine the area of a parallelogram whose diagonals are given by the vectors \( \mathbf{d_1} = 3\hat{i} + 2\hat{j} - 7\hat{k} \) and \( \mathbf{d_2} = 5\hat{i} + 6\hat{j} - 3\hat{k} \), we can follow these steps:

### Step 1: Understand the relationship between the diagonals and the area of the parallelogram.
The area \( A \) of a parallelogram can be calculated using the formula:
\[ A = \frac{1}{2} \|\mathbf{d_1} \times \mathbf{d_2}\| \]
where \( \mathbf{d_1} \) and \( \mathbf{d_2} \) are the diagonals of the parallelogram, and \( \times \) denotes the cross product.
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