The minimum number of vectors to give zero resultant is …………………………………..in one plane.

Options

A. Two
B. three
C. four
D. more than four

Answer

To determine the minimum number of vectors required to give a zero resultant in one plane, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Resultant Vectors**:
- A resultant vector is the vector sum of two or more vectors. For the resultant to be zero, the vectors must balance each other out.

2. **Considering Two Vectors**:
- Let's consider two vectors, \( \vec{A} \) and \( \vec{B} \). The resultant \( \vec{R} \) of these two vectors can be expressed as:
\[ \vec{R} = \vec{A} + \vec{B} \]

3. **Condition for Zero Resultant**:
- For the resultant \( \vec{R} \) to be zero, the following condition must be satisfied:
\[ \vec{A} + \vec{B} = 0 \]
- This implies that \( \vec{B} = -\vec{A} \). Thus, the two vectors must be equal in magnitude but opposite in direction.

4. **Magnitude and Direction**:
- If the magnitudes of \( \vec{A} \) and \( \vec{B} \) are equal, say \( |\vec{A}| = |\vec{B}| \), and the angle \( \theta \) between them is 180 degrees (anti-parallel), then the resultant will be zero.

5. **Conclusion**:
- Therefore, the minimum number of vectors required to achieve a zero resultant in one plane is **two** vectors.

### Final Answer:
The minimum number of vectors to give zero resultant in one plane is **2**.

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