The lines `(x-1)/2=(y-2)/2=(z-3)/0` and
`(x-2)/0=(y+3)/0=(z-4)/1` are parallel.

Answer

To determine whether the given lines are parallel, we can analyze their direction ratios. The lines are given in symmetric form, and we need to extract the direction ratios from each line.

### Step-by-Step Solution

1. **Identify the direction ratios of the first line**:
The first line is given as:
\[ \frac{x-1}{2} = \frac{y-2}{2} = \frac{z-3}{0} \]
From this, we can see that the direction ratios (A1, B1, C1) of the first line are:
\[ A1 = 2, \quad B1 = 2, \quad C1 = 0 \]

2. **Identify the direction ratios of the second line**:
The second line is given as:
\[ \frac{x-2}{0} = \frac{y+3}{0} = \frac{z-4}{1} \]
From this, we can see that the direction ratios (A2, B2, C2) of the second line are:
\[ A2 = 0, \quad B2 = 0, \quad C2 = 1 \]

3. **Set up the condition for parallel lines**:
For two lines to be parallel, the following condition must hold:
\[ \frac{A1}{A2} = \frac{B1}{B2} = \frac{C1}{C2} \]
Substituting the values we found:
\[ \frac{2}{0} = \frac{2}{0} = \frac{0}{1} \]

4. **Evaluate the ratios**:
We need to analyze each ratio:
- \(\frac{2}{0}\) is undefined.
- \(\frac{2}{0}\) is also undefined.
- \(\frac{0}{1} = 0\).

Since the first two ratios are undefined, we conclude that the condition for parallel lines is satisfied because both lines do not have a defined direction in the x and y components, indicating they are parallel in the z-direction.

5. **Conclusion**:
Since the condition for parallel lines is satisfied, we can conclude that the two lines are indeed parallel.