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------------------------------------------------ ATC advises that simultaneous operations are in progress at an airport. Pilots could expect a clearance to:

1. Take off over the top of an aircraft on an intersecting runway.
2. Take off on a specified parallel runway.
3. Land and hold short of an intersecting runway.
4. Land on a specified parallel runway.

The problem involves applying vector mathematics and trigonometry to determine the position vectors of two aircraft from a control tower and calculating the distance between them.

Explanation:

The question discusses simultaneous operations at an airport and asks what pilots could expect by way of a clearance in such a situation. Notably, this scenario involves air traffic control (ATC) and the positioning and movement of aircraft. The multiple choices given concern various operational clearances that a pilot might receive. However, the additional provided information relating to vectors and positions of two aircraft is an applied physics problem, specifically vector analysis and distance calculation between two moving planes.

To approach this, one would use trigonometry and vector mathematics to find the position vectors of the planes from the reference point of the control tower. Once the position vectors are determined, the distance between the Boeing 747 and the Douglas DC-3 can be found using the Pythagorean theorem or vector subtraction, followed by finding the magnitude of the resultant vector.