In the control tower at a regional airport, an air traffic controller monitors two aircraft as their positions change with respect to the control tower. One plane is a cargo carrier Boeing 747 and the other plane is a Douglas DC-3. The Boeing is at an altitude of 2,000 m, located at 15° above the horizontal, and 45° north of west, as seen by the tower. The DC-3 is at an altitude of 2,900 m, located at 5° above the horizontal, and located directly west as seen by the tower. (a) Find the position vectors of the planes relative to the control tower (in km). (Express your answers in vector form. Assume the +x-axis is to the east, the +y-axis is to the north, and the +z-axis is up towards the sky.) RBoeing km Roc-3 = km (b) What is the distance (in km) between the planes at the moment the air traffic controller makes a note about their positions? km

In the control tower at a regional airport, an air traffic controller monitors two aircraft as their positions change with respect to the control tower. One plane is a cargo carrier Boeing 747 and the other plane is a Douglas DC-3. The Boeing is at an altitude of 2,000 m, located at 15° above the horizontal, and 45° north of west, as seen by the tower. The DC-3 is at an altitude of 2,900 m, located at 5° above the horizontal, and located directly west as seen by the tower. (a) Find the position vectors of the planes relative to the control tower (in km). (Express your answers in vector form. Assume the +x-axis is to the east, the +y-axis is to the north, and the +z-axis is up towards the sky.) RBoeing km Roc-3 = km (b) What is the distance (in km) between the planes at the moment the air traffic controller makes a note about their positions? km