Let the angle between two nonzero vector `vecA and vecB` is `120^@` and its resultant be `vecC`.

Options

A. C must be equal to |A-B|
B. C must be less than |A_B|
C. C must be greater than |A-B|
D. C may be equal to |A-B|

Explanation

To solve the problem, we need to analyze the relationship between the two vectors \(\vec{A}\) and \(\vec{B}\) and their resultant vector \(\vec{C}\) when the angle between them is \(120^\circ\).

### Step 1: Understand the Resultant of Two Vectors
The resultant vector \(\vec{C}\) of two vectors \(\vec{A}\) and \(\vec{B}\) can be calculated using the formula:
\[ |\vec{C}| = \sqrt{|\vec{A}|^2 + |\vec{B}|^2 + 2|\vec{A}||\vec{B}|\cos(\theta)} \]
where \(\theta\) is the angle between the two vectors.

### Step 2: Substitute the Given Values
In this case, the angle \(\theta = 120^\circ\). We know that:
\[ \cos(120^\circ) = -\frac{1}{2} \]
Now, substituting this into the resultant formula gives:
\[ |\vec{C}| = \sqrt{|\vec{A}|^2 + |\vec{B}|^2 + 2|\vec{A}||\vec{B}| \left(-\frac{1}{2}\right)} \]
This simplifies to:
\[ |\vec{C}| = \sqrt{|\vec{A}|^2 + |\vec{B}|^2 - |\vec{A}||\vec{B}|} \]

### Step 3: Analyze the Magnitude of \(\vec{C}\)
Now, we can analyze the magnitude of \(\vec{C}\) in relation to \(|\vec{A} - \vec{B}|\). The magnitude of the difference of two vectors is given by:
\[ |\vec{A} - \vec{B}| = \sqrt{|\vec{A}|^2 + |\vec{B}|^2 - 2|\vec{A}||\vec{B}|\cos(\theta)} \]
Substituting \(\theta = 120^\circ\) into this formula gives:
\[ |\vec{A} - \vec{B}| = \sqrt{|\vec{A}|^2 + |\vec{B}|^2 + |\vec{A}||\vec{B}|} \]

### Step 4: Compare \(|\vec{C}|\) and \(|\vec{A} - \vec{B}|\)
Now we need to compare the two magnitudes:
1. For \(|\vec{C}|\):
\[ |\vec{C}| = \sqrt{|\vec{A}|^2 + |\vec{B}|^2 - |\vec{A}||\vec{B}|} \]
2. For \(|\vec{A} - \vec{B}|\):
\[ |\vec{A} - \vec{B}| = \sqrt{|\vec{A}|^2 + |\vec{B}|^2 + |\vec{A}||\vec{B}|} \]

### Step 5: Conclusion
Since \(|\vec{C}|\) has a negative term and \(|\vec{A} - \vec{B}|\) has a positive term, we can conclude that:
\[ |\vec{C}| < |\vec{A} - \vec{B}| \]
Thus, the correct answer to the options given in the question is:
- **C must be less than A - B**.