Determine which of the planes whose equations are given below are parallel and which are perpendicular. Are any of the planes the same?

a$)2$x $+3$y $$ z $=3$

b$)6$x $+4$y $2$z $+2=0$

c$)$ x $+$ y $$ z $=0$

d$)10$x $+15$y $5$z $=1$

e$)3$x $2$y $+$ z $=1$

Provide reasoning why the planes are parallel or perpendicular or same.

Find the distance between parallel planes.