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 find 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 \( \vec{A} \) can be resolved into two components: one along the x-axis and the other along the y-axis.
- If \( \alpha \) is the angle that the vector \( \vec{A} \) makes with the x-axis, then the components can be expressed as:
\[ A_x = A \cos(\alpha) \quad \text{(x-component)} \]
\[ A_y = A \sin(\alpha) \quad \text{(y-component)} \]

2. **Using the Complementary Angle**:
- Alternatively, if \( \beta \) is the angle that the vector makes with the y-axis, we can express the components as:
\[ A_x = A \sin(\beta) \quad \text{(x-component)} \]
\[ A_y = A \cos(\beta) \quad \text{(y-component)} \]
- Here, we have used the relationship \( \alpha + \beta = 90^\circ \), which implies \( \sin(\beta) = \cos(\alpha) \) and \( \cos(\beta) = \sin(\alpha) \).

3. **Maximizing the y-component**:
- To maximize the y-component \( A_y \), we need to maximize \( A \cos(\beta) \).
- The maximum value of \( \cos(\beta) \) occurs when \( \beta = 0^\circ \).

4. **Conclusion**:
- Therefore, the component of vector \( \vec{A} \) along the y-axis will have its maximum value when the vector \( \vec{A} \) is aligned with the y-axis, meaning it makes an angle of \( 0^\circ \) with the y-axis.

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

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