Find the vector equation of the following planes in cartesian form :
`" "vecr=hati-hatj+lamda(hati+hatj+hatk)+mu(hati-2hatj+3hatk)`.

Explanation

To find the vector equation of the plane in Cartesian form given by the equation \( \vec{r} = \hat{i} - \hat{j} + \lambda(\hat{i} + \hat{j} + \hat{k}) + \mu(\hat{i} - 2\hat{j} + 3\hat{k}) \), we will follow these steps:

### Step 1: Identify the point and direction vectors
From the given vector equation, we can identify:
- A point on the plane \( P \) is given by \( \hat{i} - \hat{j} \) (which corresponds to the coordinates (1, -1, 0)).
- The direction vectors of the line contained in the plane are:
- \( \vec{A} = \hat{i} + \hat{j} + \hat{k} \)
- \( \vec{B} = \hat{i} - 2\hat{j} + 3\hat{k} \)
...