Problem $5.(20$ pts$)$ Consider the plane $\backslash (\backslash$mathbf$\{$P$\}\backslash )$ with linear equation $\backslash (2$ x$+6$ y$+3$ z$=18\backslash )$

$($a$)$ Find the $\backslash ($ x$,$ y $\backslash ),$ and $\backslash ($ z $\backslash )-$intercepts.

$($b$)$ Use the result of part $($a$)$ to plot the part of the plane in the first octant $($a triangular region is enough.$)$

$($c$)$ Find symmetric equations for the line of intersection of $\backslash (\backslash$mathbf$\{$P$\}\backslash )$ with the $\backslash ($ x y $\backslash )-$plane.

$($d$)$ Find two distinct vectors parallel to $\backslash (\backslash$mathbf$\{$P$\}\backslash )$ and a vector that is normal to the two vectors.

$($e$)$ Find the line of intersection of $\backslash (\backslash$mathbf$\{$P$\}\backslash )$ with the plane $\backslash ($ y$=2$ x $\backslash ).$