If the angle between two vectors A and B is `120^(@)`, then its resultant C will be

Options

A. `C=|A-B|`
B. `Clt|A-B|`
C. `Cgt|A-B|`
D. `C=|A+B|`

Explanation

To find the resultant vector \( C \) when the angle between two vectors \( A \) and \( B \) is \( 120^\circ \), we can use the law of cosines. The law of cosines states that the magnitude of the resultant vector \( C \) can be calculated using the formula:

\[ |C| = \sqrt{|A|^2 + |B|^2 + 2|A||B|\cos(\theta)} \]

where \( \theta \) is the angle between the two vectors.

### Step-by-Step Solution:

1. **Identify the angle and vectors**: We know that the angle \( \theta = 120^\circ \).

2. **Substitute the values into the formula**: The cosine of \( 120^\circ \) is given by:
\[ \cos(120^\circ) = -\frac{1}{2} \]
Therefore, we can substitute this value into the formula:
\[ |C| = \sqrt{|A|^2 + |B|^2 + 2|A||B|(-\frac{1}{2})} \]

3. **Simplify the expression**:
\[ |C| = \sqrt{|A|^2 + |B|^2 - |A||B|} \]

4. **Analyze the options**: We need to determine which of the given options is correct based on the derived expression for \( |C| \):
- \( |C| = |A| - |B| \)
- \( |C| < |A| - |B| \)
- \( |C| > |A| - |B| \)
- \( |C| = |A| + |B| \)

5. **Evaluate the options**:
- The expression \( |C| = |A| - |B| \) would only hold true if \( \theta = 180^\circ \) (which is not the case here).
- The expression \( |C| < |A| - |B| \) is false because the resultant cannot be less than the difference of the magnitudes.
- The expression \( |C| > |A| - |B| \) is true since the resultant is always greater than the difference of the magnitudes when the angle is less than \( 180^\circ \).
- The expression \( |C| = |A| + |B| \) would only hold true if \( \theta = 0^\circ \) (which is also not the case here).

6. **Conclusion**: The correct option is that \( |C| > |A| - |B| \).

### Final Answer:
The resultant \( C \) will be greater than \( |A| - |B| \).