Given that `P+Q+R=0`. Which of the following statement is true?

Options

A. `|P|+|Q|=|R|`
B. `|P+Q|=|R|`
C. `|P|-|Q|=|R|`
D. `|P-Q|=|R|`

Explanation

To solve the problem given that \( P + Q + R = 0 \), we need to analyze the implications of this vector equation and determine which of the provided statements is true.

### Step-by-Step Solution:

1. **Understanding the Vector Equation**:
- The equation \( P + Q + R = 0 \) implies that \( R = - (P + Q) \). This means that vector \( R \) is equal in magnitude but opposite in direction to the vector sum of \( P \) and \( Q \).

2. **Visualizing the Vectors**:
- We can visualize this by drawing a triangle where the vectors \( P \) and \( Q \) are two sides of the triangle, and \( R \) is the third side, pointing in the opposite direction to the resultant of \( P \) and \( Q \).

3. **Checking the Magnitudes**:
- According to the triangle law of vector addition, the magnitude of the resultant vector (which is \( R \)) should be less than or equal to the sum of the magnitudes of the other two vectors.
- Thus, we can say:
\[ |R| = |P + Q| \leq |P| + |Q| \]

4. **Evaluating the Options**:
- **Option 1**: \( |P| + |Q| = |R| \)
- This is incorrect because the triangle inequality states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
- **Option 2**: \( P + Q = R \)
- This is incorrect because \( R = - (P + Q) \).
- **Option 3**: \( P - Q = R \)
- This is incorrect because \( R \) is not simply the difference of \( P \) and \( Q \).
- **Option 4**: \( |P| - |Q| = |R| \)
- This is also incorrect because it does not hold true in general for vectors.

5. **Conclusion**:
- After evaluating all options, we find that none of the options provided are correct based on the vector equation \( P + Q + R = 0 \).

### Final Answer:
None of the statements provided are true based on the given vector equation \( P + Q + R = 0 \).