Fill a large pot with lightly salted water and bring to a rolling boil over high heat. Stir in the linguine and return to a boil. Cook until the pasta has cooked through but is still firm to the bite, about 11 minutes.
While pasta is cooking, combine the olive oil, pineapple juice, orange juice, orange zest, lemon zest, salt, pepper and garlic in a blender. Blend on high speed until smooth.
Pour sauce into a large frypan over medium-high heat. Bring to a simmer and cook for 2 minutes. Add the prawns and parsley; cook until prawns are pink and cooked through, 3 to 5 minutes.
Drain the linguine, and place on a serving platter. Spoon the prawns and sauce over the pasta, and top with a sprinkle of Parmesan cheese.