Find the scalar and dot product of vectors `hati+2hatj-3hatk` and `2hati-hatj+hatk.`

Explanation

To find the scalar (dot) product of the vectors \( \mathbf{a} = \hat{i} + 2\hat{j} - 3\hat{k} \) and \( \mathbf{b} = 2\hat{i} - \hat{j} + \hat{k} \), we will follow these steps:

### Step 1: Identify the components of the vectors
The vectors are given as:
- \( \mathbf{a} = \hat{i} + 2\hat{j} - 3\hat{k} \) can be represented as \( (1, 2, -3) \).
- \( \mathbf{b} = 2\hat{i} - \hat{j} + \hat{k} \) can be represented as \( (2, -1, 1) \).

### Step 2: Use the formula for the dot product
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