Find the equation of a plane through the intersection of the planes ` vec rdot( hat i+3 hat j- hat k)=5a n d vec rdot(2 hat i- hat j+ hat k)=3` and passing through the point `(1,1,1)dot`

Explanation

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

### Step 1: Write the equations of the given planes

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

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