Find the area of the parallelogram whose diagonals are represented by the vectors `vec(d)_(1)=(2 hat(i) - hat(j)+ hat(k)) and vec(d)_(2) = (3 hat(i) + 4 hat(j) - hat(k)).`

Explanation

To find the area of the parallelogram whose diagonals are represented by the vectors \(\vec{d_1} = (2\hat{i} - \hat{j} + \hat{k})\) and \(\vec{d_2} = (3\hat{i} + 4\hat{j} - \hat{k})\), we can use the formula for the area of a parallelogram in terms of its diagonals.

### Step-by-Step Solution:

1. **Identify the vectors for the diagonals:**
\[ \vec{d_1} = 2\hat{i} - \hat{j} + \hat{k} \]
...