Given the lines $L_1$:$\frac{x-1}{2}=\frac{z+1}{p+2},y=2$ and $L_2$:$\frac{x+3}{-6}=\frac{z}{1},y=-1$

a$)$ What is the value of $p$ that makes the two lines perpendicular?

b$)$ What is the value of p that makes the two lines parallel?

c$)$ Can these two lines ever be caincident? Explain.