The minimum number of unequal vectors whose vector sum can be zero is

Options

A. 1
B. 2
C. 3
D. 4

Answer

To find the minimum number of unequal vectors whose vector sum can be zero, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Vectors**:
- A vector is a quantity that has both magnitude and direction. The vector sum of multiple vectors is the resultant vector obtained by adding them together.

2. **Single Vector Case**:
- If we have only one vector, it cannot sum to zero because it has a direction and magnitude. Thus, the resultant will always be equal to that vector.

3. **Two Vectors Case**:
- If we consider two unequal vectors, say \( \vec{F_1} \) and \( \vec{F_2} \), they can only cancel each other out if they are equal in magnitude and opposite in direction. Since they are unequal, their vector sum cannot be zero.

4. **Three Vectors Case**:
- Now, let’s consider three vectors \( \vec{F_1}, \vec{F_2}, \) and \( \vec{F_3} \). It is possible for three unequal vectors to sum to zero. For example, if \( \vec{F_1} \) and \( \vec{F_2} \) are in one direction, and \( \vec{F_3} \) has a magnitude equal to the sum of \( \vec{F_1} \) and \( \vec{F_2} \) but acts in the opposite direction, then their sum can be zero.

5. **Conclusion**:
- Therefore, the minimum number of unequal vectors whose vector sum can be zero is **three**.

### Final Answer:
The minimum number of unequal vectors whose vector sum can be zero is **3**.

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