Planes

Try to complete the following questions for our lesson on Monday.

1. Find a vector equation of the plane passing through \(A(1,2,3)\), \(B(3,1,-2)\), and \(C(4,4,4)\).
2. Find a vector equation of the plane with Cartesian equation \(3x+2y-z=1\).
3. Find a vector equation of the plane containing the line \[\vec{r}=\begin{bmatrix}-1\\-1\\4\end{bmatrix}+\lambda \begin{bmatrix}-2\\1\\1\end{bmatrix}\] and passing through the point \(A(6,-3,2)\).