Find the unit vector perpendicular to the plane `vecr*(2hati+hatj+2hatk)=5`.

Explanation

To find the unit vector perpendicular to the plane given by the equation \(\vec{r} \cdot (2\hat{i} + \hat{j} + 2\hat{k}) = 5\), we can follow these steps:

### Step 1: Identify the normal vector
The equation of the plane can be expressed in the form \(\vec{r} \cdot \vec{n} = d\), where \(\vec{n}\) is the normal vector to the plane. From the given equation, we can identify the normal vector \(\vec{n}\):
\[ \vec{n} = 2\hat{i} + \hat{j} + 2\hat{k} \]

...