CJC/2021/JC1/Promo/P1/Q04

The points $A(1,0,-2), B(3,-1,-2)$ and $C(-3,7,0)$ lie on plane $p_1$. Another plane $p_2$ has equation $3 x-y+2 z=3$.
(i) Find a vector equation of plane $p_1$ in the form $\mathbf{r} \cdot \mathbf{n}=d$.

[3]

(ii) Find the acute angle between $p_1$ and $p_2$.
The equation of plane $p_3$ is given to be $-9 x+3 y-6 z=7$.
(iii) Find the shortest distance between $p_2$ and $p_3$.

[3]