JPJC Tutorial Question 1(c)

Find the equation of the following planes in both the scalar product form and Cartesian form:

1. Plane passing through the point \((0,1,6)\) and parallel to the plane \(\mathbf{r}\cdot\mathrm{(}\mathbf{i}-\mathrm{2}\mathbf{j}\mathrm{)}\,\mathrm{=}\,\mathrm{3}\).[3]
2. Plane containing the points \((0,1,1)\), \((2,1,0)\) and \((-2,0,3)\).[3]
3. Plane passing through the point \((1,1,0)\) and perpendicular to the line
   \(\mathbf{r}=\mathbf{i}+3\mathbf{j}+\mathbf{k}+\alpha(5\mathbf{i}+3\mathbf{j}-2\mathbf{k}),\,\alpha \in \mathbb{R}\).[3]
4. Plane containing the point \((1,0,-1)\) and the line \(2x-1=y+2,\,z=3.\)[3]
5. Plane containing the line \(\mathbf{r}\,=\,3\mathbf{i}-2\mathbf{k}+\beta \mathbf{(i-j)},\,\,\beta \in \mathbb{R}\), and perpendicular to the plane \(2x-3y+6z=1\).[3]