Final answer:
In the context of NAV CANADA's air traffic control at YVR, the problem requires finding the position vectors of two aircraft relative to the control tower and calculating the distance between the planes using those vectors.
Step-by-step explanation:
The service provided by NAV CANADA involves air traffic control (ATC), which includes the coordination of aircraft and vehicle movements in the manoeuvring area. This service is crucial at airports like Vancouver International Airport (YVR), where the ATC unit operates from the control tower. Focusing on the mathematical part of tracking the movements of two aircraft, let's find the solution to the problem presented:
a) Position Vectors of the Planes
To find the position vectors, we assume the control tower as the origin. For the Boeing 747 climbing at 10° above the horizontal and moving 30° north of west at an altitude of 2500 m, we can calculate its position vector using trigonometric functions. Similarly, we can determine the position vector of the DC-3, which is at an altitude of 3000 m, climbing at 5° above the horizontal, and cruising directly west.
b) Distance Between the Planes
Once we have the position vectors, we can calculate the distance between the two planes using the Pythagorean theorem or vector subtraction, depending on the exact positioning of the planes relative to each other and the control tower.