The component of a vector `r` along X-axis will have maximum value if

Options

A. `vecr` is along positive y-axis
B. `vecr` is along positive x-axis
C. `vecr` makes an angle of `45^(@)` with the x-axis
D. `vecr` is along negative y-axis

Explanation

To solve the question regarding the component of a vector \( \mathbf{r} \) along the X-axis, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Vector Components**:
- A vector \( \mathbf{r} \) can be represented in a two-dimensional plane (XY-plane) where it makes an angle \( \theta \) with the positive X-axis.
- The components of the vector \( \mathbf{r} \) can be expressed as:
- \( r_x = r \cos \theta \) (component along the X-axis)
- \( r_y = r \sin \theta \) (component along the Y-axis)

2. **Finding the Maximum Component along X-axis**:
- We need to determine when the component \( r_x = r \cos \theta \) reaches its maximum value.
- The cosine function \( \cos \theta \) varies between -1 and 1.

3. **Maximizing \( \cos \theta \)**:
- The maximum value of \( \cos \theta \) occurs when \( \theta = 0^\circ \).
- At \( \theta = 0^\circ \), \( \cos 0^\circ = 1 \), thus:
\[ r_x = r \cdot 1 = r \]
- This means that the component of vector \( \mathbf{r} \) along the X-axis is maximized when the vector is aligned with the positive X-axis.

4. **Conclusion**:
- Therefore, the component of vector \( \mathbf{r} \) along the X-axis will have its maximum value when \( \mathbf{r} \) is along the positive X-axis.

### Final Answer:
The component of vector \( \mathbf{r} \) along the X-axis will have maximum value if \( \mathbf{r} \) is along the positive X-axis.