State the parallelogram law of vector addition Derive the
expressions for magnitude and direction of the resultant vector.
[Oct Nov. 2018 EEE March April 2017 EEE):
2016 (DOD: Apnia 2012 CME)
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State the parallelogram law of vector addition Derive the
expressions for magnitude and direction of the resultant vector.
[Oct Nov. 2018 EEE March April 2017 EEE):
2016 (DOD: Apnia 2012 CME)
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Answer:
This is basic vector work and is in all the text books (or all those I’ve looked at over the years) in some shape or form. It is often popularly known as ‘tip-to-tail’ vector addition.
The parallelogram rule or law describes how to add two vectors (it can be extended to any number of vectors). The vectors do not need to be ‘in contact’ with each other. Any vector can be translated without its magnitude and direction changing. For example in the diagram above, the vector CD has been translated (represented by the red arrow) to a new position where C (the tail of CD) is placed on B (the tip of AB). Neither magnitude or direction of CD has been changed in the translation. AB and CD could have started out anywhere else on the page and translated so that they both started at the origin. As long as neither was changed in any way their magnitudes and directions are unchanged; they have been translated. A vector of magnitude 10 units at a bearing of 045 can be moved bodily to the origin (ie. translated) and it will still have magnitude 10 units and a bearing of 045 at the origin.
Let there be two vectors AB and CD (as in the diagram above). AB has magnitude 10 units and a bearing of 045 while CD has magnitude 5 units and a bearing of 090. AB and CD are drawn as starting at (0,0) but they could have been anywhere on the page and simply translated to the origin.
PROCEDURE: (a) translate (represented by the red arrow) the vector CD so that the tail C is placed on the tip B of vector AB (hence … ‘tip-to-tail’).
(b) draw the resultant vector AD (in green in the diagram)
(c) Either measure or calculate the magnitude of AD and its bearing.
Explanation:
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