This topic belongs to the interest of surveying engineer. The curvature of earth is to be taken into account, which is one of the main causes for the complexity of the problem. There are other methods existing for the same purpose, like trigonometric equations, charts, etc. But the approach of this method is unique. In this paper, earth is assumed as a sphere. The origin of Cartesian co-ordinate system is placed at the centre of the earth. A plane passing through North Pole, centre of the earth, and a station (position of observer) is oriented. This plane will trace a great circle. A unit tangential vector pointing towards north is placed at the station. Similarly, another plane is passed through the station, centre of the earth and the desired city, resulting another great circle. Another unit tangential vector is placed along second great circle at the same point. Vector approach is used to determine the angle between two unit vectors, and that is the required azimuth. The distance between two points i.e. station and city is also evaluated.