Let `overset(rarr)C = overset(rarr)A+overset(rarr)B` then :

Options

A. `|overset(rarr)C|` is always greater then `|overset(rarr)A|`
B. it is possible to have and `|overset(rarr)C| lt |overset(rarr)B|`
C. `|overset(rarr)C|` is always equal to `|overset(rarr)A + overset(rarr)B|`
D. `|overset(rarr)C|` is never equal to `|overset(rarr)A+overset(rarr)B|`

Explanation

To solve the problem, we need to analyze the vector equation given:

\[ \overset{\rarr}{C} = \overset{\rarr}{A} + \overset{\rarr}{B} \]

We will evaluate the options based on vector properties.

### Step 1: Understanding the vector addition
The equation states that vector \( \overset{\rarr}{C} \) is the resultant of vectors \( \overset{\rarr}{A} \) and \( \overset{\rarr}{B} \). According to the triangle law of vector addition, the magnitude of the resultant vector \( C \) can be expressed in terms of the magnitudes of \( A \) and \( B \).

### Step 2: Applying the triangle inequality
From the triangle inequality, we know that:
\[ |\overset{\rarr}{A}| + |\overset{\rarr}{B}| > |\overset{\rarr}{C}| \]
This implies that the sum of the magnitudes of vectors \( A \) and \( B \) is always greater than the magnitude of vector \( C \).

### Step 3: Analyzing the options
1. **Option A**: \( |\overset{\rarr}{C}| \) is always greater than \( |\overset{\rarr}{A}| \).
- This is not necessarily true, as \( |\overset{\rarr}{C}| \) can be less than \( |\overset{\rarr}{A}| \) if \( \overset{\rarr}{B} \) is in the opposite direction of \( \overset{\rarr}{A} \).

2. **Option B**: \( |\overset{\rarr}{C}| \) can be less than \( |\overset{\rarr}{B}| \).
- This is possible if \( \overset{\rarr}{A} \) is in the opposite direction to \( \overset{\rarr}{B} \) and has a greater magnitude. Thus, this option can be correct.

3. **Option C**: \( |\overset{\rarr}{C}| \) is always equal to \( |\overset{\rarr}{A}| + |\overset{\rarr}{B}| \).
- This is incorrect because equality holds only when \( \overset{\rarr}{A} \) and \( \overset{\rarr}{B} \) are in the same direction.

4. **Option D**: \( |\overset{\rarr}{C}| \) is never equal to \( |\overset{\rarr}{A}| + |\overset{\rarr}{B}| \).
- This is also incorrect because \( |\overset{\rarr}{C}| \) can equal \( |\overset{\rarr}{A}| + |\overset{\rarr}{B}| \) when both vectors are in the same direction.

### Conclusion
The correct option is **Option B**: \( |\overset{\rarr}{C}| \) can be less than \( |\overset{\rarr}{B}| \).