Find the vector equation of a plane passing through the intersection of the planes `vecr.(hati+hatj+hatk) = 6` and `vecr. (2hati+3hatj+4hatk) - 5 = 0` and through the point `(2,2,1)`.

Explanation

To find the vector equation of a plane passing through the intersection of two given planes and a specific point, we can follow these steps:

### Step 1: Write the equations of the given planes.
The equations of the two planes are:
1. \( \vec{r} \cdot (\hat{i} + \hat{j} + \hat{k}) = 6 \)
2. \( \vec{r} \cdot (2\hat{i} + 3\hat{j} + 4\hat{k}) - 5 = 0 \)

### Step 2: Express the equation of the plane through the intersection.
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