Find the Cartesian form of the equation of the following plane: ` vec r=( hat i- hat j)+s(- hat i+ hat j+2 hat k)+t( hat i+2 hat j+ hat k)dot`

Explanation

To find the Cartesian form of the equation of the given plane, we will follow these steps:

### Step 1: Identify the given vector equation
The vector equation of the plane is given as:
\[ \vec{r} = \hat{i} - \hat{j} + s(-\hat{i} + \hat{j} + 2\hat{k}) + t(\hat{i} + 2\hat{j} + \hat{k}) \]

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