Evaluate the product `(3 vec a-5 vec b).(2 vec a+7 vec b)`

Explanation

To evaluate the product \((3 \vec{a} - 5 \vec{b}) \cdot (2 \vec{a} + 7 \vec{b})\), we will follow the steps of the dot product calculation systematically.

### Step-by-Step Solution:

1. **Write the Expression**:
\[ (3 \vec{a} - 5 \vec{b}) \cdot (2 \vec{a} + 7 \vec{b}) \]
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