The component of a vector `vecA` along y-axis will have maximum value if

Options

A. `vecA` makes an angle of 30° with y-axis
B. `vecA` makes an angle of 60° with y-axis
C. `vecA` makes an angle of 0° with y-axis
D. `vecA` makes an angle of 90° with y-axis

Answer

To determine the maximum value of the component of a vector \( \vec{A} \) along the y-axis, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Vector Components**:
A vector can be resolved into its components along the coordinate axes. For a vector \( \vec{A} \), we can find its component along the y-axis.

2. **Using Trigonometric Functions**:
The component of the vector \( \vec{A} \) along the y-axis can be expressed as:
\[ A_y = A \cdot \cos(\theta) \]
where \( A \) is the magnitude of the vector \( \vec{A} \) and \( \theta \) is the angle between the vector \( \vec{A} \) and the y-axis.

3. **Finding the Maximum Value**:
To maximize \( A_y \), we need to maximize the term \( \cos(\theta) \). The cosine function reaches its maximum value of 1 when \( \theta = 0^\circ \).

4. **Conclusion**:
Therefore, the component of the vector \( \vec{A} \) along the y-axis will have its maximum value when the angle \( \theta \) is \( 0^\circ \). This means that the vector \( \vec{A} \) is aligned perfectly with the y-axis.

### Final Answer:
The component of the vector \( \vec{A} \) along the y-axis will have a maximum value if the vector makes an angle of \( 0^\circ \) with the y-axis.

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