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

Options

A. `alphaltbeta`
B. `alphaltbeta if A ltB`
C. `alphaltbeta if Altbeta`
D. `alphaltbet if A=B.`

Answer

To solve the problem, we need to analyze the relationship between two vectors, \(\vec{A}\) and \(\vec{B}\), and their resultant vector \(\vec{R}\). The angles \(\alpha\) and \(\beta\) are defined as the angles between the resultant vector and the vectors \(\vec{A}\) and \(\vec{B}\), respectively.

### Step 1: Understand the Vectors and Resultant
We have two vectors, \(\vec{A}\) and \(\vec{B}\). The resultant vector \(\vec{R}\) can be expressed as:
\[ \vec{R} = \vec{A} + \vec{B} \]
The angles \(\alpha\) and \(\beta\) are defined as:
- \(\alpha\): the angle between \(\vec{R}\) and \(\vec{A}\)
- \(\beta\): the angle between \(\vec{R}\) and \(\vec{B}\)

### Step 2: Analyze the Angles
According to the problem, if \(|\vec{A}| < |\vec{B}|\), then \(\alpha < \beta\). This means that the resultant vector \(\vec{R}\) is closer to vector \(\vec{B}\) than to vector \(\vec{A}\).

### Step 3: Consider the Magnitudes of Vectors
If \(|\vec{A}| > |\vec{B}|\), then \(\alpha > \beta\). This indicates that the resultant vector \(\vec{R}\) is closer to vector \(\vec{A}\) than to vector \(\vec{B}\).

### Step 4: Conclusion
From the above analysis, we can conclude:
- If \(|\vec{A}| < |\vec{B}|\), then \(\alpha < \beta\).
- If \(|\vec{A}| > |\vec{B}|\), then \(\alpha > \beta\).

Thus, the correct option is that \(\alpha\) is less than \(\beta\) when \(|\vec{A}| < |\vec{B}|\).