Assertion: Vecot `(hati+hatj+hatk)` is perpendicular to `(hati-2hatj+hatk)`
Reason: Two non-zero vectors are perpendicular if their dot product is equal to zero.

Explanation

To determine whether the assertion and reason provided in the question are correct, we will follow these steps:

### Step 1: Understand the Assertion
The assertion states that the vector \( \hat{i} + \hat{j} + \hat{k} \) is perpendicular to the vector \( \hat{i} - 2\hat{j} + \hat{k} \).

### Step 2: Understand the Reason
The reason states that two non-zero vectors are perpendicular if their dot product is equal to zero.

### Step 3: Calculate the Dot Product
To check if the vectors are perpendicular, we need to calculate the dot product of the two vectors.

Let:
- \( \mathbf{A} = \hat{i} + \hat{j} + \hat{k} \)
- \( \mathbf{B} = \hat{i} - 2\hat{j} + \hat{k} \)

The dot product \( \mathbf{A} \cdot \mathbf{B} \) is calculated as follows:

\[ \mathbf{A} \cdot \mathbf{B} = (\hat{i} + \hat{j} + \hat{k}) \cdot (\hat{i} - 2\hat{j} + \hat{k}) \]

Using the properties of dot product, we expand this:

\[ = \hat{i} \cdot \hat{i} + \hat{i} \cdot (-2\hat{j}) + \hat{i} \cdot \hat{k} + \hat{j} \cdot \hat{i} + \hat{j} \cdot (-2\hat{j}) + \hat{j} \cdot \hat{k} + \hat{k} \cdot \hat{i} + \hat{k} \cdot (-2\hat{j}) + \hat{k} \cdot \hat{k} \]

Calculating each term:
- \( \hat{i} \cdot \hat{i} = 1 \)
- \( \hat{i} \cdot (-2\hat{j}) = 0 \)
- \( \hat{i} \cdot \hat{k} = 0 \)
- \( \hat{j} \cdot \hat{i} = 0 \)
- \( \hat{j} \cdot (-2\hat{j}) = -2 \)
- \( \hat{j} \cdot \hat{k} = 0 \)
- \( \hat{k} \cdot \hat{i} = 0 \)
- \( \hat{k} \cdot (-2\hat{j}) = 0 \)
- \( \hat{k} \cdot \hat{k} = 1 \)

Now, summing these results:

\[ \mathbf{A} \cdot \mathbf{B} = 1 + 0 + 0 + 0 - 2 + 0 + 0 + 0 + 1 = 1 - 2 + 1 = 0 \]

### Step 4: Conclusion
Since the dot product \( \mathbf{A} \cdot \mathbf{B} = 0 \), the vectors \( \hat{i} + \hat{j} + \hat{k} \) and \( \hat{i} - 2\hat{j} + \hat{k} \) are indeed perpendicular.

### Final Conclusion
Both the assertion and the reason are correct. The reason correctly explains why the assertion is true.