If P,Q are (2,5,-7), (-3,2,1) respectively then what are the direction rations of the line PQ?

Options

A. `lt10,6,-16gt`
B. `lt5,3,8gt`
C. `lt-5,-3,-8gt`
D. None of these

Answer

To find the direction ratios of the line segment joining points P and Q, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Coordinates**:
- Let \( P = (x_1, y_1, z_1) = (2, 5, -7) \)
- Let \( Q = (x_2, y_2, z_2) = (-3, 2, 1) \)

2. **Use the Formula for Direction Ratios**:
The direction ratios of the line segment \( PQ \) can be calculated using the formula:
\[ \text{Direction Ratios} = (x_2 - x_1, y_2 - y_1, z_2 - z_1) \]

3. **Calculate the Direction Ratios**:
- For the x-coordinate:
\[ x_2 - x_1 = -3 - 2 = -5 \]
- For the y-coordinate:
\[ y_2 - y_1 = 2 - 5 = -3 \]
- For the z-coordinate:
\[ z_2 - z_1 = 1 - (-7) = 1 + 7 = 8 \]

4. **Combine the Results**:
Therefore, the direction ratios of the line segment \( PQ \) are:
\[ (-5, -3, 8) \]

### Final Answer:
The direction ratios of the line PQ are \( (-5, -3, 8) \).

---