Find the scalr and vector products of two vectors ` vec a =(3 hat I - 4 hat j + 5 hat k) and `vec b = (-2 hat I + hat j- 3 hat k).

Explanation

To find the scalar and vector products of the vectors \(\vec{a} = (3 \hat{i} - 4 \hat{j} + 5 \hat{k})\) and \(\vec{b} = (-2 \hat{i} + \hat{j} - 3 \hat{k})\), we will follow these steps:

### Step 1: Calculate the Scalar Product (Dot Product)

The scalar product (dot product) of two vectors \(\vec{a}\) and \(\vec{b}\) is given by:
\[ \vec{a} \cdot \vec{b} = a_x b_x + a_y b_y + a_z b_z \]
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