Three forms of a plane in four settings

Find the vector equations of the plane $\Pi$ in parametric form and scalar product form, and also the Cartesian equation of the plane $\Pi$ if

(a) $\Pi$ passes through the three points $A(1,0,2)$, $B(0,1,3)$, $C(2,-1,4)$.

(b) $\Pi$ contains the two lines $l_1:\mathbf r=(1+\lambda)\mathbf i+(1+2\lambda)\mathbf j-\lambda\mathbf k$, $\lambda\in\mathbb R$, and $l_2:\mathbf r=(2-\mu)\mathbf i+\mu\mathbf j+(2-2\mu)\mathbf k$, $\mu\in\mathbb R$.

(c) $\Pi$ contains the point $D(1,-1,2)$ and the line $l:\mathbf r=(1+3\lambda)\mathbf i-(1+2\lambda)\mathbf j+6\lambda\mathbf k$, $\lambda\in\mathbb R$.

(d) $\Pi$ contains the point $A(1,0,2)$ and parallel to the y-z plane.