The direction ratios of a line passing through the points A(1,2,6) and B(-4,5,0) are

Options

A. `-1,3,-4`
B. `-6,2,-4`
C. `-5,3,-6`
D. `-2,-3,-5`

Answer

To find the direction ratios of the line passing through the points A(1, 2, 6) and B(-4, 5, 0), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the coordinates of points A and B**:
- Point A has coordinates \( A(1, 2, 6) \).
- Point B has coordinates \( B(-4, 5, 0) \).

2. **Calculate the direction ratios**:
- The direction ratios of the line can be found by calculating the vector \( \overrightarrow{AB} \), which is given by the formula:
\[ \overrightarrow{AB} = B - A \]
- This means we will subtract the coordinates of point A from the coordinates of point B:
\[ \overrightarrow{AB} = (-4 - 1, 5 - 2, 0 - 6) \]

3. **Perform the calculations**:
- For the x-coordinate:
\[ -4 - 1 = -5 \]
- For the y-coordinate:
\[ 5 - 2 = 3 \]
- For the z-coordinate:
\[ 0 - 6 = -6 \]

4. **Write the direction ratios**:
- Therefore, the direction ratios of the line \( \overrightarrow{AB} \) are:
\[ (-5, 3, -6) \]

### Final Answer:
The direction ratios of the line passing through the points A(1, 2, 6) and B(-4, 5, 0) are \( (-5, 3, -6) \).

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