How many minimum number of vectors in different planes can be added to give zero resultant ?

Options

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

Answer

To determine the minimum number of vectors in different planes that can be added to give a zero resultant, we can analyze the problem step by step.

### Step-by-Step Solution:

1. **Understanding Vectors and Planes**:
- Vectors can exist in different planes. A vector in a plane can be represented as having both magnitude and direction.
- When vectors are in the same plane, they can easily be added or subtracted to find a resultant.

2. **Adding Two Vectors**:
- If we consider two vectors, they must be in the same plane to have a resultant of zero. If they are in different planes, they cannot cancel each other out because they do not share a common plane of action.

3. **Introducing a Third Vector**:
- Adding a third vector to two vectors in different planes does not help in achieving a zero resultant. The third vector cannot counterbalance the effect of the two vectors in different planes.

4. **Considering Four Vectors**:
- When we introduce a fourth vector, we can arrange the vectors such that three of them lie in one plane, and the fourth vector lies in a different plane.
- The three vectors in the same plane can be arranged such that their resultant is equal in magnitude and opposite in direction to the fourth vector in the different plane.

5. **Conclusion**:
- Therefore, the minimum number of vectors required in different planes to achieve a zero resultant is **four**. Three vectors can be in one plane, and one vector can be in another plane, allowing for a balance that results in zero.

### Final Answer:
The minimum number of vectors in different planes that can be added to give a zero resultant is **four**.