Minimum number of two coplanar vectors of equal magnitude whose vectors sum could be zero, is:

Options

A. 2
B. 3
C. 4
D. more than 4

Answer

To solve the problem of finding the minimum number of two coplanar vectors of equal magnitude whose vector sum could be zero, follow these steps:

### Step-by-Step Solution:

1. **Understand Coplanar Vectors**:
- Coplanar vectors are vectors that lie in the same plane. This means that they can be represented geometrically on a two-dimensional plane.

2. **Equal Magnitude Condition**:
- The problem states that the vectors must have equal magnitude. Let’s denote the magnitude of each vector as \( k \).

3. **Vector Sum Equals Zero**:
- For the sum of vectors to equal zero, the vectors must be arranged in such a way that they cancel each other out. This can happen if two vectors are equal in magnitude but opposite in direction.

4. **Consider Two Vectors**:
- If we take two vectors \( \vec{A} \) and \( \vec{B} \) such that \( \vec{A} = k \) and \( \vec{B} = -k \) (where \( -k \) indicates that \( \vec{B} \) is in the opposite direction to \( \vec{A} \)), the vector sum can be calculated as:
\[ \vec{A} + \vec{B} = k + (-k) = 0 \]
- This shows that two coplanar vectors of equal magnitude can indeed sum to zero.

5. **Check for More Vectors**:
- While it is possible to have more than two vectors that can also sum to zero (for example, three vectors at angles of 120 degrees to each other, or four vectors arranged in a square), the question specifically asks for the minimum number.

6. **Conclusion**:
- Therefore, the minimum number of two coplanar vectors of equal magnitude whose vector sum could be zero is **2**.

### Final Answer:
The minimum number of two coplanar vectors of equal magnitude whose vector sum could be zero is **2**.