It's not clear to me what your method is here, but your result doesn't seem correct.
Your result contains the point (3,0,1) and also (just picking a random point in the plane) (1,2,1); and therefor the vector (3,0,1)-(1,2,1)=(2,-2,0) is parallel to your plane.
Now, the plane [itex]\Pi_1[/itex] contains the points (1,-1,7) and (0,-7,0), so the vector (1,-1,7)-(0,-7,0)=(1,6,7) is parallel to [itex]\Pi_1[/itex].
If your plane were really perpendicular to [itex]\Pi_1[/itex], then any vector parallel to your plane would be perpendicular to any vector parallel to [itex]\Pi_1[/itex] and hence you would expect [itex](2,-2,0)\cdot(1,6,7)[/itex] to be zero; but it clearly isn't.
If you explain your reasoning for each step, and state your reults for parts (i) through (iii), I may be able to see where you are going wrong. A jumbled mess of equations, without any explanation is not a solution.
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