Three observers A, B and C measure the speed of light coming from a source to be `v_A,v_B` and `v_C`. The observer A moves towards the source and C moves away from the soure at the same speed. The observer B stays stationary. The surrounding space is vacuum everywhere .

Options

A. `upsilon_A gt upsilon_B gt upsilon_C`
B. `upsilon_A lt upsilon_B lt upsilon_C`
C. `upsilon_A = upsilon_B = upsilon_C`
D. `upsilon_B = (1)/(2) (upslion_A + upsilon_c).`

Answer

To solve the problem, we need to analyze the situation involving the three observers A, B, and C, and their measurements of the speed of light.

### Step-by-Step Solution:

1. **Understanding the Situation**:
- Observer A is moving towards the light source.
- Observer C is moving away from the light source.
- Observer B is stationary.
- The speed of light in a vacuum is denoted as \( c \).

2. **Applying the Principle of Relativity**:
- According to Einstein's theory of relativity, the speed of light in a vacuum is constant and is the same for all observers, regardless of their motion relative to the light source.
- Therefore, the speed of light measured by each observer should be the same.

3. **Setting Up the Equations**:
- Let \( v_A \) be the speed of light measured by observer A, \( v_B \) by observer B, and \( v_C \) by observer C.
- Based on the principle of relativity, we can write:
\[ v_A = v_B = v_C = c \]

4. **Analyzing the Observers' Movements**:
- Observer A, moving towards the source, might intuitively seem to measure a higher speed of light, but according to relativity, this is not the case.
- Observer C, moving away from the source, might seem to measure a lower speed of light, but again, relativity dictates that the speed remains \( c \).

5. **Conclusion**:
- Therefore, we conclude that:
\[ v_A = v_B = v_C = c \]
- This means that all observers measure the speed of light as \( c \), regardless of their motion.

### Final Answer:
The relationship between the velocities measured by the three observers is:
\[ v_A = v_B = v_C = c \]