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Unit Vector Relations via Direction Cosines


Affiliations
1 Rajasthan Institute of Engineering and Technology (RIET), Jaipur (Rajashan), India
 

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.

Keywords

Cartesian, coordinate system, vector conversion, dot product, electromagnetism, rectangular, spherical, direction cosines, unit vector.
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  • Unit Vector Relations via Direction Cosines

Abstract Views: 77  |  PDF Views: 21

Authors

Sandeep Kumar Bairwa
Rajasthan Institute of Engineering and Technology (RIET), Jaipur (Rajashan), India
Rohit Hansaliya
, India
Nikhll Samaliya
, India
Monica Lambha
, India
Altamash Anwar
, India

Abstract


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.

Keywords


Cartesian, coordinate system, vector conversion, dot product, electromagnetism, rectangular, spherical, direction cosines, unit vector.

References





DOI: https://doi.org/10.21843/reas%2F2021%2F57-61%2F212374