The projection of a line segment on the coordinate axes are 2,3,6. Then the length of the line segment is

Options

A. 7
B. 5
C. 1
D. 11

Explanation

To find the length of the line segment given its projections on the coordinate axes, we can use the formula that relates the projections to the length of the line segment in three-dimensional space.

### Step-by-Step Solution:

1. **Identify the Projections**:
The projections of the line segment on the coordinate axes are given as:
- Projection on x-axis = 2
- Projection on y-axis = 3
- Projection on z-axis = 6

2. **Use the Length Formula**:
The length \( L \) of the line segment can be calculated using the formula:
\[ L = \sqrt{(x^2 + y^2 + z^2)} \]
where \( x, y, z \) are the projections on the x, y, and z axes respectively.

3. **Substitute the Values**:
Substitute the values of the projections into the formula:
\[ L = \sqrt{(2^2 + 3^2 + 6^2)} \]

4. **Calculate Each Square**:
- \( 2^2 = 4 \)
- \( 3^2 = 9 \)
- \( 6^2 = 36 \)

5. **Add the Squares**:
Now add these values together:
\[ L = \sqrt{(4 + 9 + 36)} = \sqrt{49} \]

6. **Find the Square Root**:
Finally, calculate the square root:
\[ L = 7 \]

### Conclusion:
The length of the line segment is \( 7 \).

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