- #1
runningc
- 9
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How do I calculate the resultant of three component vectors set mutually at 60 degrees to each other (not in the same plane)?
3D coordinates vector calculation
- Context: Undergrad
- Thread starter runningc
- Start date
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- Tags
- 3d Calculation Coordinates Vector
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Discussion Overview
The discussion centers around calculating the resultant of three component vectors that are mutually oriented at 60 degrees to each other and not confined to the same plane. The focus includes methods of vector addition and representation in Cartesian coordinates.
Discussion Character
- Technical explanation, Mathematical reasoning
Main Points Raised
- One participant inquires about the method for calculating the resultant of three component vectors set at 60 degrees to each other.
- Another participant suggests using Cartesian coordinates to resolve each vector along x, y, and z axes, and then summing the components for the resultant vector.
- A further contribution emphasizes that the resultant magnitude can be found by adding the magnitudes in quadrature and that the angular direction may require resolving to angular representations, potentially using Euler angles.
- Some participants express a preference for leaving the vectors in component form, arguing it is simpler and more useful unless a graphical representation is needed.
- A participant references a Wikipedia article as a good introductory resource on Euclidean vectors.
Areas of Agreement / Disagreement
There is no consensus on a single method for calculating the resultant, as participants present different approaches and preferences regarding vector representation.
Contextual Notes
Participants do not clarify specific assumptions regarding the coordinate system or the definitions of the vectors involved, and there are no resolved mathematical steps provided in the discussion.
- #2
sophiecentaur
Science Advisor
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Hi and welcome to PF.
The most straightforward way would be to use Cartesian Co-ordinates and resolve each of the three vectors along arbitrary x, y and z axes and add the x components together and likewise for the y and z components. Then the overall resultant vector is given by adding the three resulting components.
The most straightforward way would be to use Cartesian Co-ordinates and resolve each of the three vectors along arbitrary x, y and z axes and add the x components together and likewise for the y and z components. Then the overall resultant vector is given by adding the three resulting components.
- #3
Cutter Ketch
- 982
- 446
sophiecentaur said:
Where, of course, “adding the three resulting components” is vector addition. The resultant magnitude is found by adding the magnitudes in quadrature and the angular direction requires resolving to some angular representation, probably Euler angles, by appropriate trigonometry.
Frankly I’d just leave it as components. It’s easier, just as meaningful and twice as useful. (for those of us who favor linear algebra)
- #4
sophiecentaur
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Agreed - unless you actually need to draw a line on a graph.Cutter Ketch said:
- #5
berkeman
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And the Wikipedia article is a pretty good introduction:
https://en.wikipedia.org/wiki/Euclidean_vector
https://en.wikipedia.org/wiki/Euclidean_vector
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