A good application for vector analysis is the calculation of an airplane's flight path. This requires knowing the magnitude and direction of both the plane's thrust, as well as that of the prevailing winds acting on the plane.
If a plane is trying to fly to an airstrip 50 miles north of its current location, and it is travelling at 100 mph, a person might assume the plane would arrive in 30 minutes if the pilot pointed the plane due north. But if the plane had a prevailing wind from the west blowing at 10 miles per hour, it would end up 5 miles to the east of the airport, as the wind has blown the airplane off course.
Think of the plane's speed and direction as vector A, and the wind's speed and direction as vector B. Add them head to foot, then draw a line from the plane's starting point to the end of vector B. This is the actual location of the plane.
Winds blowing at the plane from the front are called headwinds, while winds from the back of the plane are called tailwinds. All winds from any direction are calculated as vectors, and these vectors affect aircraft courses and require consistent course correction.