The minimum number of vectors of equal magnitude required to produce a zero resultant is :

Options

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

Answer

To determine the minimum number of vectors of equal magnitude required to produce a zero resultant, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Vectors**: A vector has both magnitude and direction. To achieve a zero resultant, the vectors must cancel each other out.

2. **Equal Magnitude Requirement**: We are told that the vectors must have equal magnitudes. This means if we have a vector A with magnitude 'a', any other vector we use must also have the same magnitude 'a'.

3. **Opposite Directions**: For two vectors to cancel each other out, they must be directed opposite to each other. For example, if we have vector A pointing in one direction, we can have another vector B pointing in the exact opposite direction.

4. **Minimum Number of Vectors**: The simplest case is to consider two vectors. If we take one vector A and another vector B of equal magnitude but in the opposite direction, the resultant vector will be:
\[ \vec{R} = \vec{A} + (-\vec{A}) = 0 \]
This shows that two vectors are sufficient to produce a zero resultant.

5. **Conclusion**: Therefore, the minimum number of vectors of equal magnitude required to produce a zero resultant is **2**.