Show that the point `(1,2,1)` is equidistant from the planes `vecr.(hati+2hatj-2hatk) = 5` and `vecr.(2hati-2hatj+hatk) + 3 = 0`.

Explanation

To show that the point \( (1, 2, 1) \) is equidistant from the planes given by the equations \( \vec{r} \cdot (\hat{i} + 2\hat{j} - 2\hat{k}) = 5 \) and \( \vec{r} \cdot (2\hat{i} - 2\hat{j} + \hat{k}) + 3 = 0 \), we will calculate the distances from the point to both planes and verify if they are equal.

### Step 1: Identify the normal vectors and the equations of the planes
The first plane can be rewritten in the standard form:
\[ \vec{r} \cdot (\hat{i} + 2\hat{j} - 2\hat{k}) = 5 \implies x + 2y - 2z - 5 = 0 \]
The coefficients are:
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