In a clockwise system :-

Options

A. `hatjxxhatk =hati`
B. `hatk.hati=1`
C. `hati.hati=0`
D. `hatjxxhatj=1`

Explanation

To solve the question regarding the properties of vectors in a clockwise system, we will analyze each option step by step.

### Step 1: Analyze Option 1 - \( \mathbf{j} \times \mathbf{k} = \mathbf{i} \)
- The cross product of two vectors follows the right-hand rule.
- If we point the fingers of our right hand in the direction of \( \mathbf{j} \) and curl them towards \( \mathbf{k} \), the thumb will point in the direction of \( \mathbf{i} \).
- Therefore, \( \mathbf{j} \times \mathbf{k} = \mathbf{i} \) is **true**.

### Step 2: Analyze Option 2 - \( \mathbf{k} \cdot \mathbf{i} = 1 \)
- The dot product of two unit vectors is equal to the cosine of the angle between them.
- The angle between \( \mathbf{k} \) and \( \mathbf{i} \) is \( 90^\circ \), and \( \cos(90^\circ) = 0 \).
- Therefore, \( \mathbf{k} \cdot \mathbf{i} = 0 \), making this option **false**.

### Step 3: Analyze Option 3 - \( \mathbf{i} \cdot \mathbf{i} = 0 \)
- The dot product of a vector with itself is equal to the square of its magnitude.
- Since \( \mathbf{i} \) is a unit vector, \( \mathbf{i} \cdot \mathbf{i} = 1 \).
- Therefore, this option is **false**.

### Step 4: Analyze Option 4 - \( \mathbf{j} \times \mathbf{j} = 1 \)
- The cross product of any vector with itself is always zero.
- Thus, \( \mathbf{j} \times \mathbf{j} = 0 \), making this option **false**.

### Conclusion
- The only true statement among the options provided is Option 1: \( \mathbf{j} \times \mathbf{k} = \mathbf{i} \).

### Final Answer
**The correct answer is Option 1: \( \mathbf{j} \times \mathbf{k} = \mathbf{i} \).**

---