If `hati, hatj and hatk` are three mutually perpendicular vectors, then find the value of `hatj. (hatkxx hati).`

Answer

To solve the problem, we need to find the value of \( \hat{j} \cdot (\hat{k} \times \hat{i}) \).

### Step-by-Step Solution:

1. **Identify the vectors**: We have three mutually perpendicular unit vectors: \( \hat{i} \), \( \hat{j} \), and \( \hat{k} \).

2. **Calculate the cross product \( \hat{k} \times \hat{i} \)**:
- The cross product of two unit vectors that are perpendicular to each other can be calculated using the right-hand rule.
- According to the right-hand rule, \( \hat{k} \times \hat{i} = \hat{j} \).

3. **Substitute the result of the cross product into the dot product**:
- Now we need to compute \( \hat{j} \cdot \hat{j} \).

4. **Calculate the dot product \( \hat{j} \cdot \hat{j} \)**:
- The dot product of a unit vector with itself is equal to 1.
- Therefore, \( \hat{j} \cdot \hat{j} = 1 \).

5. **Final Result**:
- Thus, the value of \( \hat{j} \cdot (\hat{k} \times \hat{i}) \) is \( 1 \).

### Summary:
The final answer is \( 1 \).