Vector and Cartesian equations of planesAQA A-Level Further Maths: Mind map

Exam questions on Vector and Cartesian equations of planes

1. The plane $\Pi$ has vector equation $\mathbf r=\begin{pmatrix} 1 \\ 0 \\ 2 \end{pmatrix}+\lambda\begin{pmatrix} 1 \\ 2 \\ 0 \end{pmatrix}+\mu\begin{pmatrix} 0 \\ 3 \\ 1 \end{pmatrix}$.
   Determine whether the point $(3,4,2)$ lies on $\Pi$.2 marks
2. The points $A(1,2,0)$, $B(3,2,1)$ and $C(2,5,2)$ lie in a plane $\Pi$.
   Hence find a Cartesian equation of $\Pi$.2 marks
3. The plane $\Pi$ has Cartesian equation $3x-2y+z=12$.
   Find a vector equation of $\Pi$ in the form $\mathbf r=\mathbf a+\lambda\mathbf b+\mu\mathbf c$.3 marks