Find the volume of a parallelepiped whose edges are given by `-3 hat i+7 hat j-5 hat k ,-5 hat i+7 hat j-` 3` hat ka n d7 hat i-5 hat j-3 hat kdot`

Explanation

To find the volume of the parallelepiped formed by the vectors given, we can use the scalar triple product, which is calculated using the determinant of a matrix formed by the vectors. Here are the steps to solve the problem:

### Step 1: Define the Vectors
Let the vectors be defined as follows:
- **Vector A**: \( \mathbf{a} = -3 \hat{i} + 7 \hat{j} - 5 \hat{k} \)
- **Vector B**: \( \mathbf{b} = -5 \hat{i} + 7 \hat{j} - 3 \hat{k} \)
- **Vector C**: \( \mathbf{c} = 7 \hat{i} - 5 \hat{j} - 3 \hat{k} \)

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