QUESTION

Dr$.$ Shahzad, a brilliant inventor from Pakistan, has recently designed a futuristic flying machine, while Captain Bilal has crafted an advanced submersible capable of deep$-$sea exploration. Both inventors, with their innovative spirit and determination, are eager to showcase their creations at the upcoming World Inventors' Fair.

Dr$.$ Shahzad's Flying Machine: Dr$.$ Shahzad's flying machine has a wingspan of $22$ feet, a height of $42$ feet, a weight of $10$ tons, and a fuel capacity of $1$ gallon.

Captain Bilal's Submersible: Captain Bilal's submersible boasts a streamlined design with a length of $20$ feet, a height of $36$ feet, a weight of $8$ tons, and an oxygen supply of $0$ cubic feet $($ideally$).$

$($A$)$ In the tale of Dr$.$ Shahzad's Flying Machine and Captain Bilal's Submersible, what is the shortest straight$-$line distance between the two innovative inventions when considering all four dimensions $($wingspan$,$ height, weight, and fuel$/$oxygen capacity$)?$

$($B$)$ When navigating from Dr$.$ Shahzad's Flying Machine to Captain Bilal's Submersible, summing the absolute differences of their coordinates across the four dimensions, what is the total distance one might need to travel along this path?

$($C$)$ Using a generalized distance metric that balances between the Norm$-1$ and Norm$-2$ distances, what is the overall distance between Dr$.$ Shahzad's Flying Machine and Captain Bilal's Submersible with a parameter $q=3?$

$($D$)$ What is the maximum absolute difference between any single dimension $($wingspan$.$ height, weight, or fuel$/$oxygen capacity$)$ of Dr$.$ Shahzad's Flying Machine and Captain Bilal's Submersible, indicating the most pronounced difference between the two innovative inventions?