The minimum number of vector having different planes which can be added to give zero resultant is

Options

A. 2
B. 3
C. 4
D. 5

Explanation

To determine the minimum number of vectors in different planes that can be added to give a zero resultant, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Concept of Vectors in Different Planes:**
- Vectors can exist in three-dimensional space, which consists of three planes: the XY plane, the XZ plane, and the YZ plane. Each vector can lie in one of these planes.

2. **Identifying the Minimum Requirement:**
- To achieve a zero resultant, we need to ensure that the vectors cancel each other out. This requires careful consideration of their directions and magnitudes.

3. **Drawing Vectors in Different Planes:**
- Let's denote the vectors as follows:
- Vector A in the XY plane.
- Vector B in the YZ plane.
- Vector C in the XZ plane.
- Initially, we can visualize three vectors, one in each of the three planes.

4. **Analyzing the Resultant:**
- When we add these three vectors, the resultant vector will not necessarily be zero. The resultant will depend on the magnitudes and directions of the vectors.

5. **Adding a Fourth Vector:**
- To achieve a zero resultant, we can introduce a fourth vector (let's call it Vector D) that is equal in magnitude but opposite in direction to the resultant of the first three vectors.
- This fourth vector can be placed in any of the three planes, but it must be directed such that it cancels out the resultant of the first three vectors.

6. **Conclusion:**
- Therefore, the minimum number of vectors required to achieve a zero resultant in different planes is **four**.

### Final Answer:
The minimum number of vectors having different planes which can be added to give zero resultant is **4**.