Separate a unique triple intersection from a common line

The planes $p_1,p_2,p_3$ are $2x-5y+3z=3$, $3x+2y-5z=-5$, $5x+\lambda y+17z=\mu$, respectively. Here $\lambda,\mu$ are constants. When $\lambda=-20.9$, $\mu=16.6$, find x,y,z satisfying all three equations.

The first two planes meet in a line l.

(i) Find a vector equation of l.

(ii) If $p_3$ contains l, find $\lambda,\mu$.

(iii) If instead $p_3$ does not intersect l, what can be said about $\lambda,\mu$?

(iv) Find a Cartesian equation of the plane containing l and $(1,-1,3)$.