The line, joining the points `(1,2,3)(-1,-2,-3)` is parallel to to the line joining points `(-2,1,5),(3,3,2)`.

Answer

To determine whether the line joining the points \( A(1, 2, 3) \) and \( B(-1, -2, -3) \) is parallel to the line joining the points \( C(-2, 1, 5) \) and \( D(3, 3, 2) \), we will follow these steps:

### Step 1: Find the direction ratios of line AB
The direction ratios of a line joining two points \( (x_1, y_1, z_1) \) and \( (x_2, y_2, z_2) \) can be calculated using the formula:
\[ \text{Direction Ratios} = (x_2 - x_1, y_2 - y_1, z_2 - z_1) \]
For points \( A(1, 2, 3) \) and \( B(-1, -2, -3) \):
- \( x_2 - x_1 = -1 - 1 = -2 \)
- \( y_2 - y_1 = -2 - 2 = -4 \)
- \( z_2 - z_1 = -3 - 3 = -6 \)

Thus, the direction ratios for line AB are:
\[ A_1 = -2, \quad B_1 = -4, \quad C_1 = -6 \]

### Step 2: Find the direction ratios of line CD
For points \( C(-2, 1, 5) \) and \( D(3, 3, 2) \):
- \( x_2 - x_1 = 3 - (-2) = 5 \)
- \( y_2 - y_1 = 3 - 1 = 2 \)
- \( z_2 - z_1 = 2 - 5 = -3 \)

Thus, the direction ratios for line CD are:
\[ A_2 = 5, \quad B_2 = 2, \quad C_2 = -3 \]

### Step 3: Check the condition for parallel lines
Two lines are parallel if the ratios of their direction ratios are equal:
\[ \frac{A_1}{A_2} = \frac{B_1}{B_2} = \frac{C_1}{C_2} \]
Substituting the values we found:
\[ \frac{-2}{5}, \quad \frac{-4}{2}, \quad \frac{-6}{-3} \]

Calculating these ratios:
- \( \frac{-2}{5} \) remains as is.
- \( \frac{-4}{2} = -2 \).
- \( \frac{-6}{-3} = 2 \).

### Step 4: Compare the ratios
Now we compare:
\[ \frac{-2}{5} \neq -2 \quad \text{and} \quad \frac{-2}{5} \neq 2 \]
Since the ratios are not equal, we conclude that the lines are not parallel.

### Conclusion
The line joining the points \( (1, 2, 3) \) and \( (-1, -2, -3) \) is **not parallel** to the line joining the points \( (-2, 1, 5) \) and \( (3, 3, 2) \).

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