If `hati,hatj` and `hatk` are unit vectors along X,Y `&` Z axis respectively, then tick the wrong statement:

Options

A. `hati*hati= 1`
B. `hatixxhatj= hatk`
C. `hati*hatj=0`
D. `hatixxhatk=-hati`

Answer

To solve the problem, we need to analyze the statements regarding the unit vectors \( \hat{i}, \hat{j}, \) and \( \hat{k} \) along the X, Y, and Z axes respectively. We will check each statement to identify the incorrect one.

### Step-by-step Solution:

1. **Understanding Unit Vectors**:
- The unit vectors \( \hat{i}, \hat{j}, \hat{k} \) are defined as:
- \( \hat{i} \) is a unit vector along the X-axis.
- \( \hat{j} \) is a unit vector along the Y-axis.
- \( \hat{k} \) is a unit vector along the Z-axis.
- The magnitude of each unit vector is 1:
\[ |\hat{i}| = |\hat{j}| = |\hat{k}| = 1 \]

2. **Analyzing the Statements**:
- **Statement 1**: \( \hat{i} \cdot \hat{i} = 1 \)
- The dot product of a vector with itself gives the square of its magnitude.
- Therefore, \( \hat{i} \cdot \hat{i} = |\hat{i}|^2 = 1^2 = 1 \) (True)

- **Statement 2**: \( \hat{i} \times \hat{j} = \hat{k} \)
- Using the right-hand rule, the cross product \( \hat{i} \times \hat{j} \) gives a vector that is perpendicular to both \( \hat{i} \) and \( \hat{j} \), which is \( \hat{k} \).
- Therefore, \( \hat{i} \times \hat{j} = \hat{k} \) (True)

- **Statement 3**: \( \hat{i} \cdot \hat{j} = 0 \)
- The dot product of two perpendicular vectors is zero.
- Since \( \hat{i} \) and \( \hat{j} \) are perpendicular, \( \hat{i} \cdot \hat{j} = 0 \) (True)

- **Statement 4**: \( \hat{i} \times \hat{k} = -\hat{j} \)
- Using the right-hand rule, \( \hat{i} \times \hat{k} \) actually gives \( \hat{j} \), not \( -\hat{j} \).
- Therefore, \( \hat{i} \times \hat{k} = \hat{j} \) (False)

3. **Conclusion**:
- The incorrect statement is **Statement 4**: \( \hat{i} \times \hat{k} = -\hat{j} \).

### Final Answer:
The wrong statement is: **Statement 4**.