Which of the following is not a property of a null vector ?

Options

A. `vecA = vec0`
B. `lambda vec0 = vec0` where `lambda` is a scalar
C. `0vecA = vecA`
D. `vecA - vecA = vec0`

Explanation

To solve the question "Which of the following is not a property of a null vector?", we need to first understand the properties of a null vector.

### Step-by-Step Solution:

1. **Definition of Null Vector**:
- A null vector is defined as a vector with a magnitude of zero. It has no direction. In mathematical terms, it can be represented as \( \vec{A} = 0 \hat{i} + 0 \hat{j} + 0 \hat{k} \).

**Hint**: Remember that a null vector is characterized by its zero magnitude and lack of direction.

2. **Properties of Null Vector**:
- **Magnitude**: The magnitude of a null vector is always zero.
- **Addition**: Adding a null vector to any other vector results in the other vector itself. For example, \( \vec{A} + \vec{0} = \vec{A} \).
- **Multiplication by Scalar**: Multiplying a null vector by any scalar results in a null vector. For example, \( k \cdot \vec{0} = \vec{0} \) for any scalar \( k \).
- **Multiplication by Another Vector**: If you multiply a null vector by any vector, the result is still a null vector. For example, \( \vec{0} \cdot \vec{B} = \vec{0} \).

**Hint**: List out the properties of null vectors to identify which statement does not fit.

3. **Analyzing the Options**:
- Now we look at the provided options (not specified in the question but inferred from the transcript):
1. Vector \( \vec{A} = 0 \) (True)
2. Multiplying a null vector by any scalar results in zero (True)
3. If we multiply a null vector by another vector, we get the original vector (False)
4. Multiplying a null vector by zero gives a null vector (True)

**Hint**: Compare each option against the properties of null vectors to find the incorrect statement.

4. **Conclusion**:
- The statement that says multiplying a null vector by another vector gives the original vector is incorrect. Therefore, this option is not a property of a null vector.

**Final Answer**: The option that states "If we multiply a null vector by another vector, we get the original vector" is not a property of a null vector.