Transformations for 10
The equations for a line and plane in vector form may be
useful.
Line: ${\bf r}={\bf a} + \lambda{\bf b}$
Plane: ${\bf r}={\bf a} + \lambda{\bf b}+ \mu{\bf c}$
It may also be useful to recall that matrix multiplication is
distributive:
${\bf M}({\bf a} + {\bf b}) = {\bf Ma} + {\bf Mb}$
This problem uses concepts met in
the later Further Pure Maths A
level modules.