The equations of two straight lines are
`(x-1)/2=(y+3)/1=(z-2)/(-3)` and `(x-2)/1=(y-1)/(-3)=(z+3)/2`
Statement 1: The given lines are coplanar.
Statement 2: The equations
`2r-s=1`
`r+3s=4`
`3r+2s=5`
are consistent.

Options

A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1.
B. Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.
C. Statement-1 is True, Statement-2 is False.
D. Statement-1 is False, Statement-2 is True.

Explanation

To solve the problem, we need to analyze the two given lines and determine if they are coplanar. We will also check the consistency of the given equations.

### Step 1: Write the equations of the lines in parametric form.

The first line is given by:
\[ \frac{x-1}{2} = \frac{y+3}{1} = \frac{z-2}{-3} \]
Let \( r \) be the parameter for this line. Then, we can express the coordinates as:
\[ x = 2r + 1, \quad y = r - 3, \quad z = -3r + 2 \]

The second line is given by:
\[ \frac{x-2}{1} = \frac{y-1}{-3} = \frac{z+3}{2} \]
Let \( s \) be the parameter for this line. Then, we can express the coordinates as:
\[ x = s + 2, \quad y = -3s + 1, \quad z = 2s - 3 \]

### Step 2: Set the parametric equations equal to find conditions for intersection.

For the lines to intersect, the coordinates must be equal:
1. \( 2r + 1 = s + 2 \)
2. \( r - 3 = -3s + 1 \)
3. \( -3r + 2 = 2s - 3 \)

### Step 3: Rearranging the equations.

From the first equation:
\[ 2r - s = 1 \quad \text{(Equation 1)} \]

From the second equation:
\[ r + 3s = 4 \quad \text{(Equation 2)} \]

From the third equation:
\[ 3r + 2s = 5 \quad \text{(Equation 3)} \]

### Step 4: Check the consistency of the equations.

We have the following system of equations:
1. \( 2r - s = 1 \)
2. \( r + 3s = 4 \)
3. \( 3r + 2s = 5 \)

To check for consistency, we can solve the first two equations and substitute into the third.

From Equation 1, we can express \( s \):
\[ s = 2r - 1 \]

Substituting \( s \) into Equation 2:
\[ r + 3(2r - 1) = 4 \\ r + 6r - 3 = 4 \\ 7r - 3 = 4 \\ 7r = 7 \\ r = 1 \]

Now substituting \( r = 1 \) back to find \( s \):
\[ s = 2(1) - 1 = 1 \]

### Step 5: Verify with the third equation.

Substituting \( r = 1 \) and \( s = 1 \) into Equation 3:
\[ 3(1) + 2(1) = 5 \\ 3 + 2 = 5 \]
This holds true.

### Conclusion:

Since all three equations are consistent, we conclude that the lines are coplanar.

### Final Statements:
- **Statement 1**: The given lines are coplanar. **True**
- **Statement 2**: The equations are consistent. **True**

Thus, both statements are true.