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 $A(6,-3,2)$.