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

Options

A. `|overset(rarr)C|` is always greater then `|overset(rarr)A|` and `|overset(rarr)C| lt |overset(rarr)B|`
B. it is possible to have
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 question `overset(rarr)C = overset(rarr)A + overset(rarr)B`, we will analyze the vector addition using the triangle law of vector addition.

### Step-by-Step Solution:

1. **Understanding Vector Addition**:
- The equation `overset(rarr)C = overset(rarr)A + overset(rarr)B` indicates that vector C is the resultant of vectors A and B.
- According to the triangle law of vector addition, if you place vector A and vector B such that the tail of vector B is at the head of vector A, the resultant vector C will be drawn from the tail of vector A to the head of vector B.

2. **Visual Representation**:
- Draw vector A and vector B such that they are connected head-to-tail. This means you start from the tail of vector A and draw vector B from the head of vector A.
- The resultant vector C will be represented as the line connecting the tail of A to the head of B.

3. **Magnitude of Vectors**:
- The magnitude of a vector is its length. Let's denote:
- |A| = magnitude of vector A
- |B| = magnitude of vector B
- |C| = magnitude of vector C
- According to the triangle inequality, the magnitude of the resultant vector C must satisfy the following conditions:
- |C| < |A| + |B| (the sum of the lengths of any two sides of a triangle is greater than the length of the third side)
- |C| can be equal to |A| + |B| only when vectors A and B are in the same direction.

4. **Conclusion**:
- From the triangle law, we conclude that:
- |C| is always less than or equal to |A| + |B|.
- |C| can never be greater than |A| + |B|, and it can be equal only when A and B are collinear and in the same direction.
- Therefore, the correct statements regarding the relationship between the magnitudes of these vectors are:
- |C| < |A| + |B|
- |C| = |A| + |B| (only when A and B are in the same direction)
- |C| > |A| is not always true.

### Summary of Correct Options:
- The correct options based on the analysis are:
- |C| < |A| + |B|
- |C| = |A| + |B| (under specific conditions)