Build an intersection line and a perpendicular plane

Planes $\pi_1,\pi_2$ have equations $\mathbf r\cdot(0,1,2)=2$, $\mathbf r\cdot(2,-1,4)=12$. A=(7,2,0), O is the origin.

(i) Verify A lies in both planes.1 mark

(ii) They meet in line L. Show that a vector equation of L is $\mathbf r=(7,2,0)+\lambda(3,2,-1)$, $\lambda\in\mathbb R$.2 marks

(iii) B=(7,−4,9), and N is its perpendicular foot onto $\pi_2$. Find N.3 marks

(iv) Find the Cartesian equation of $\pi_3$ containing L and perpendicular to $\pi_2$.3 marks