Find the vector of length 3 unit which is perpendicular to `hati+hatj+hatk` and lies in the plane of `hati+hatj+hatk and 2hati-3hatj`

Explanation

To find a vector of length 3 units that is perpendicular to the vector \( \hat{i} + \hat{j} + \hat{k} \) and lies in the plane defined by the vectors \( \hat{i} + \hat{j} + \hat{k} \) and \( 2\hat{i} - 3\hat{j} \), we can follow these steps:

### Step 1: Define the vectors
Let:
- \( \mathbf{A} = \hat{i} + \hat{j} + \hat{k} \)
- \( \mathbf{B} = 2\hat{i} - 3\hat{j} \)

### Step 2: Find the normal vector to the plane
...