Unit Vector Relations via Direction Cosines

Conversion of a vector from a coordinate system to another is done via the dot product operation. Unit vector relationships have been either studied by the vector projection method or by a set of complex geometric relationship. Both of these conventional methods are rather lengthy & time-consuming and are moreover difficult to recall. In this paper, through a step by step approach employing direction cosines, the authors were able to find the unit vector conversions between the rectangular and the spherical system efficiently. A densely labelled graph showing all variable relations is required from which the results precipitate coincidentally.