If the resultant of `vecA` and `vecB` makes angle `alpha` with `vecA` and `beta` with `vecB`, then

Options

A. `alpha lt beta` always
B. `alpha lt beta` if `A lt B `
C. `alpha lt beta` if `A gt B`
D. `alpha lt beta` if A=B

Explanation

To solve the problem, we need to analyze the relationship between the vectors \(\vec{A}\) and \(\vec{B}\) and their resultant \(\vec{R}\). We are given that the angle \(\alpha\) is formed between \(\vec{A}\) and \(\vec{R}\), and the angle \(\beta\) is formed between \(\vec{B}\) and \(\vec{R}\).

### Step-by-Step Solution:

1. **Understanding the Angles**:
- The angle \(\alpha\) is the angle between vector \(\vec{A}\) and the resultant vector \(\vec{R}\).
- The angle \(\beta\) is the angle between vector \(\vec{B}\) and the resultant vector \(\vec{R}\).

2. **Using the Parallelogram Law**:
- According to the parallelogram law of vector addition, the resultant vector \(\vec{R}\) can be represented as:
\[ \vec{R} = \vec{A} + \vec{B} \]
- The angles \(\alpha\) and \(\beta\) can be analyzed based on the magnitudes of \(\vec{A}\) and \(\vec{B}\).

3. **Comparing the Angles**:
- If \(|\vec{A}| > |\vec{B}|\), the resultant vector \(\vec{R}\) will be closer to \(\vec{A}\) than to \(\vec{B}\), leading to the conclusion that \(\alpha < \beta\).
- Conversely, if \(|\vec{A}| < |\vec{B}|\), then \(\beta < \alpha\).

4. **Conclusion**:
- The problem states that \(\alpha < \beta\). This implies that the magnitude of \(\vec{A}\) must be greater than the magnitude of \(\vec{B}\):
\[ |\vec{A}| > |\vec{B}| \]
- Therefore, the correct relationship is:
\[ \text{If } \alpha < \beta, \text{ then } |\vec{A}| > |\vec{B}| \]

### Final Answer:
The resultant of \(\vec{A}\) and \(\vec{B}\) makes angle \(\alpha\) with \(\vec{A}\) and angle \(\beta\) with \(\vec{B}\), where \(\alpha < \beta\) implies that \(|\vec{A}| > |\vec{B}|\).