Evaluate the product `(3 veca-5 vecb)cdot(2 veca+7 vecb)`

Explanation

To evaluate the product \((3 \vec{a} - 5 \vec{b}) \cdot (2 \vec{a} + 7 \vec{b})\), we will use the distributive property of the dot product.

### Step-by-Step Solution:

1. **Apply the Distributive Property**:
\[ (3 \vec{a} - 5 \vec{b}) \cdot (2 \vec{a} + 7 \vec{b}) = 3 \vec{a} \cdot 2 \vec{a} + 3 \vec{a} \cdot 7 \vec{b} - 5 \vec{b} \cdot 2 \vec{a} - 5 \vec{b} \cdot 7 \vec{b} \]
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