Statement - 1 : A particle moves with a constant velocity parallel to the x-axis. Its angular momentum w.r.t. the origin will remains constant.
Because
Statement - 2 : Angular momentum is defined as `vec(L) = vec(r) xx vec(P)`

Options

A. Statement - 1 is true, statement - 2 is true, statement - 2 is correct explanation for statement - 1
B. Statement - 1 is true, Statement - 2 is true, Statement - 2 is not a correct explanation for statement - 1
C. statement - 1 is true, statement - 2 is false
D. statement - 1 is false, statement - 2 is true.

Answer

To solve the problem, we need to analyze the two statements provided and understand the relationship between the motion of the particle and its angular momentum.

### Step-by-Step Solution:

1. **Understanding the Motion of the Particle**:
- The particle is moving with a constant velocity parallel to the x-axis. This means that its speed and direction are not changing over time.

2. **Defining Angular Momentum**:
- Angular momentum (L) of a particle with respect to a point (in this case, the origin) is defined as:
\[ \vec{L} = \vec{r} \times \vec{P} \]
- Here, \(\vec{r}\) is the position vector from the origin to the particle, and \(\vec{P}\) is the linear momentum of the particle, which is given by \(\vec{P} = m\vec{v}\), where \(m\) is the mass and \(\vec{v}\) is the velocity.

3. **Analyzing the Angular Momentum**:
- The magnitude of angular momentum can be expressed as:
\[ L = mv r \sin(\theta) \]
- In this equation, \(r\) is the distance from the origin to the line of action of the velocity vector, and \(\theta\) is the angle between \(\vec{r}\) and \(\vec{v}\).

4. **Constant Parameters**:
- Since the particle is moving with constant velocity, both \(m\) (mass) and \(\vec{v}\) (velocity) are constant.
- The distance \(r\) from the origin to the line of action of the velocity vector remains constant as the particle moves parallel to the x-axis.

5. **Conclusion on Angular Momentum**:
- Since \(m\), \(v\), \(r\), and \(\theta\) remain constant throughout the motion, the angular momentum \(L\) will also remain constant. Therefore, Statement 1 is true.

6. **Explanation of Statement 2**:
- Statement 2 provides the definition of angular momentum, which supports the conclusion drawn in Statement 1. Thus, Statement 2 is a correct explanation for Statement 1.

### Final Conclusion:
- Both statements are true, and Statement 2 is the correct explanation for Statement 1.

### Answer:
- The answer is (A): Both statements are true, and Statement 2 is the correct explanation for Statement 1.

---