Wow! This really is laughable.
This question is part of the Oxford Year 2 Textbook for Further Maths. It has 3 pairs of planes for question 2, the question has the title "Find the perpendicular distance between each of these pairs of planes. Give your answers to 3 significant figures."
I believe all 3 pairs have an incorrect solution in the back of the textbook, if someone would be willing to confirm...
First Part:
Plane 1: 3x - y + 9z = 15
Plane 2: 6x - 2y + 18z = 3
I believe the answer is 1.42 to 3 significant figures, the textbook says 1.49 (I checked on Maths Stack Exchange and they seem to believe the textbook is incorrect).
Second part:
What I've listed here
Third part:
Okay so the equation given for the first plane is x + 3y - 5z = 12 and for the second plane 2x - 6y + 10z = -13
These planes aren't perpendicular, so I'm going to assume the first plane was instead meant to be -x + 3y - 5z = 12.
Even in this case the textbook's answer for the distance is different, 3.13 units is its answer, whereas wolfram says 0.93!!
This is actually laughably bad from the textbook. 3 incorrect answers in a row I believe!