Find the volume of the parallelopiped whose coterminus edges are given by vectors `2hat(i)+3hat(j)-4hat(k),5hat(i)+7hat(j)+5hat(k)and4hat(i)+5hat(j)-2hat(k)`.

Explanation

To find the volume of the parallelepiped formed by the vectors \( \mathbf{A} = 2\hat{i} + 3\hat{j} - 4\hat{k} \), \( \mathbf{B} = 5\hat{i} + 7\hat{j} + 5\hat{k} \), and \( \mathbf{C} = 4\hat{i} + 5\hat{j} - 2\hat{k} \), we can use the scalar triple product formula. The volume \( V \) of the parallelepiped is given by the absolute value of the scalar triple product of the vectors:

\[ V = |\mathbf{A} \cdot (\mathbf{B} \times \mathbf{C})| \]

### Step 1: Calculate the cross product \( \mathbf{B} \times \mathbf{C} \)

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