Intersections and distances involving planesAQA A-Level Further Maths: Mind map

Exam questions on Intersections and distances involving planes

1. The plane $\Pi$ has equation $2x-y+2z=9$ and the point $A$ has coordinates $(1,2,0)$.
   Find the coordinates of the image of $A$ when it is reflected in $\Pi$.2 marks
2. The line $l$ has equation $\mathbf r=\begin{pmatrix}1 \\ -2 \\ 3\end{pmatrix}+t\begin{pmatrix}2 \\ 1 \\ -1\end{pmatrix}$ and the plane $\Pi$ has equation $3x-y+2z=17$.
   The line $m$ has equation $\mathbf r=\begin{pmatrix}0 \\ 1 \\ 1\end{pmatrix}+s\begin{pmatrix}1 \\ -1 \\ -2\end{pmatrix}$. Show that $m$ does not meet $\Pi$.2 marks
3. The line $L$ has equation $\dfrac{x-1}{2}=\dfrac{y+3}{1}=\dfrac{z-2}{-3}$ and the plane $\Pi$ has equation $x-2y+z=3$.
   Find the coordinates of the point where $L$ meets $\Pi$.3 marks