Hugh Manatee is a mission designer at NASADA who has a passion for photography. When NASADA's social media team wanted to collect some glamor shots of the NASADA space center for recruiting purposes, Hugh volunteered to fly a drone to get some aerial photos. To Hugh's delight, planning a drone's flight path wasn't that different from vector algebra after all... The inertial reference frame is an x, y, z coordinate system. The vertical coordinate, altitude, is the z-axis. The drone is released from the origin 0 = (0,0,0). The drone needs to fly to point A, where A = 3000* + 2000+10002 feet. a. What is the total distance traveled by the drone? b. Hugh Manatee is positioned along the x-axis to control the drone, which has position vector A. How far along the drone's flight path (in feet) is Hugh at this point? In other words, calculate the magnitude of the vector projection of C onto A, where C = 2000 ft is Hugh's position. c. What is the total ground distance traveled by the drone? Calculate the vector projection of A onto the x-y plane. d. A primed reference frame x', y', z' is generated from the unprimed system x,y,z by a rotation of /2 about the z axis. The new unit vectors are ',',2' and they are related to the old unit vectors *,, 2 by: 2' = 2 Find the forms of A and C referenced to the new primed coordinate system. . e. Find the scalar product A C in the new primed coordinate system. 2