The resultant of `vecA and vecB` makes an angle `alpha` with `vecA` and `beta and vecB`,

Options

A. `alpha` is always less then `beta`
B. `alphaltbeta` if `AltB`
C. `alphaltbeta` if `AgtB`
D. `alphaltbeta` if `A=B`

Explanation

To solve the problem, we need to analyze the relationship between the angles α and β and the magnitudes of the vectors A and B.

### Step-by-Step Solution:

1. **Understanding the Problem**: We are given two vectors, A and B, and their resultant vector R makes an angle α with vector A and an angle β with vector B. We need to determine the relationships between these angles and the magnitudes of the vectors.

2. **Using the Law of Cosines**:
- The resultant vector R can be expressed in terms of its components along A and B.
- We can write:
\[ R \cos(\alpha) = A \quad \text{(1)} \]
\[ R \cos(\beta) = B \quad \text{(2)} \]

3. **Analyzing the Angles**:
- We know that the cosine function is a decreasing function in the range of 0 to 180 degrees. This means if α < β, then cos(α) > cos(β).

4. **Relating the Magnitudes**:
- From equations (1) and (2), we can express the magnitudes of A and B in terms of R:
\[ A = R \cos(\alpha) \quad \text{(3)} \]
\[ B = R \cos(\beta) \quad \text{(4)} \]
- Since cos(α) > cos(β) when α < β, we can conclude:
\[ A > B \quad \text{(5)} \]

5. **Conclusion**:
- Therefore, if α < β, it implies that vector A is greater than vector B.
- This leads us to the conclusion that the correct option is that α is less than β if A is greater than B.

### Final Answer:
The correct option is: **α is less than β if A is greater than B.**