Accessible Formulas for Computing the Magnitude of Resultant Vector in 2 and 3-Dimensions

O.E. Ikuemuya¹

Section:Research Paper, Product Type: Journal-Paper
Vol.9 , Issue.1 , pp.7-13, Feb-2022

Online published on Feb 28, 2022

Copyright © O.E. Ikuemuya . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
This paper presents accessible alternative formulas for solving geometry related problems associated with the use of Pythagoras theorem in calculating the magnitude of resultant vectors in geometry. The proposed formulas are simple and less cumbersome than the normal Pythagoras theorem when used in computing the magnitude of the resultant vector in 2 or 3-dimensions. The usage of the new formulas does not require finding the square roots of numbers which is most times very difficult to obtain without a calculator especially when the numbers involved are not perfect squares, hence its usage will drastically reduce the occurrence of irrational numbers namely square roots of non-perfect squares e.g in mathematics, since the square root of such non-perfect squares numbers usually occur when the Pythagoras theorem is applied in geometrical computations. The proposed formulas only make use of basic arithmetic operation such as addition, division and multiplication which can be done seamlessly with or without the use of calculators and it produces results that agree quite well with the results obtained using the usual Pythagoras? theorem. Also, in this paper, it was shown that the sum of the magnitude of the opposite side and adjacent side of a right-angle triangle or the sum of the magnitude of two vectors acting perpendicularly in 2-dimensions is reduced by an average constant factor of 0.7 to give the magnitude of the resultant vector or the length of the hypotenuse, and in 3-dimensions, the sum of the magnitude of the 3 vectors acting perpendicularly is been reduced by an average constant factor of 0.6 to give the magnitude of the resultant vector.

Key-Words / Index Term :
Average constant factor, Pythagoras theorem, Magnitude of resultant factor, Ikuemuyas formula

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