The parametric equation of the line is $$x=2t+1, y=3t-1,z=t+2$$
The plane it is parallel to is $$x-by+2bz = 6 $$
My approach so far
I know that i need to dot the equation of the normal with the equation of the line = 0
$$n = <1,-b,2b>$$
I would think that the equation of the line is $$ L(t) = <2t+1,3t-1,t+2>$$ but am not sure because it hasn't work out very well so far.
** Solve for b such that the parametric equation of the line is parallel to the plane