A private airplane left the airport at 1pm with speed 150 mph and its direction was 30 degrees east of north. At 3pm, the airplane reached point A and then changed its speed to 100 mph heading west. At 7pm, it reached point B. The pilot decided to change its direction to 20 degrees east of south, without changing its speed. At 9pm, the plane reached point C. Use OA = ax i + ay j to represent the displacement of the plane from 1pm to 3pm. Use AB = bx i + by j to represent the displacement of the plane from 7pm to 9pm. Use OC = dx i + dy j to represent the position of the plane at 9pm, i.e., the displacement from 1pm to 9pm, measured from the airport. We take East as positive x-direction and North as positive y-direction.