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runningc
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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
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In summary, the most straightforward way to calculate the resultant of three component vectors set at 60 degrees to each other is to use Cartesian Co-ordinates and resolve each vector along arbitrary x, y, and z axes. Then, the overall resultant vector can be found by adding the resulting components through vector addition. The magnitude of the resultant can be calculated by adding the magnitudes in quadrature, and the angular direction can be determined using appropriate trigonometry, such as Euler angles. However, it may be easier and more useful to leave the resultant as components, especially for those who prefer linear algebra. A helpful resource for understanding Euclidean vectors is the Wikipedia article.
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sophiecentaur
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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
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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)
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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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Related to 3D coordinates vector calculation
1. What is a 3D coordinate vector?
A 3D coordinate vector is a mathematical representation of a point in three-dimensional space. It consists of three components - x, y, and z - that specify the point's position relative to an origin point. This vector can be used to describe the location, direction, and magnitude of a point in 3D space.
2. How do you calculate the magnitude of a 3D coordinate vector?
The magnitude of a 3D coordinate vector can be calculated using the Pythagorean theorem. The formula is: magnitude = √(x^2 + y^2 + z^2), where x, y, and z are the components of the vector. This gives the length of the vector from its origin to its endpoint.
3. What is the dot product of two 3D coordinate vectors?
The dot product of two 3D coordinate vectors is a scalar value that represents the projection of one vector onto the other. It is calculated by multiplying the corresponding components of the two vectors and then adding them together. The formula is: A · B = Ax * Bx + Ay * By + Az * Bz, where A and B are the two vectors and Ax, Ay, Az and Bx, By, Bz are their respective components.
4. How do you find the angle between two 3D coordinate vectors?
The angle between two 3D coordinate vectors can be calculated using the dot product formula and the magnitude formula. The formula is: cosθ = (A · B) / (|A| * |B|), where A and B are the two vectors and |A| and |B| are their respective magnitudes. The angle can then be found by taking the inverse cosine of the result.
5. How can 3D coordinate vectors be used in computer graphics?
3D coordinate vectors are commonly used in computer graphics to represent and manipulate objects in a three-dimensional space. They are used to determine the position, orientation, and movement of objects in a 3D scene. They are also used in lighting and shading calculations to create realistic 3D images.
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