Find the vector equation of the plane passing through the intersection of the planes` vecr cdot(2 hat i+2 hat j-3 hat k)=7, vecr cdot(2 hat i+5 hat j+3 hat k)=9`and through the point (2, 1, 3).

Explanation

To find the vector equation of the plane passing through the intersection of the given planes and through the point (2, 1, 3), we will follow these steps:

### Step 1: Identify the equations of the given planes
The equations of the two planes are given as:
1. \( \vec{r} \cdot (2\hat{i} + 2\hat{j} - 3\hat{k}) = 7 \) (Plane P1)
2. \( \vec{r} \cdot (2\hat{i} + 5\hat{j} + 3\hat{k}) = 9 \) (Plane P2)

### Step 2: Write the equations of the planes in standard form
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