Determine the value of `alpha` for which the vectors `i-3alphahatj+hatk and hati+hatj+hatk` are parallel.

Explanation

To determine the value of \( \alpha \) for which the vectors \( \mathbf{A} = \hat{i} - 3\alpha \hat{j} + \hat{k} \) and \( \mathbf{B} = \hat{i} + \hat{j} + \hat{k} \) are parallel, we can follow these steps:

### Step 1: Identify the components of the vectors
The vector \( \mathbf{A} \) has components:
- \( A_x = 1 \) (coefficient of \( \hat{i} \))
- \( A_y = -3\alpha \) (coefficient of \( \hat{j} \))
- \( A_z = 1 \) (coefficient of \( \hat{k} \))

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