About

Single vector in 3D view

With every activation of the random vector button a vector arrow with random orientation is generated. Starting at the origin, its endpoint has random integer coordinates x,y,z. They are displayed in three editable number fields. There the coordinates may be changed to any rational number. An alternative one can draw the arrowhead in 2 dimensions with the mouse.

The range of the coordinate system is ∓ 5. A transparent coordinate mesh forms the background of the vector. The code for the generation of coordinate x is

x = integer(10*random( ) - 5).

A button with/no xyz projections shows or hides projections of the arrow onto the coordinate planes.

Five different radio buttons view select among a number of different distinct projections. Of them the 2D projections are especially suited to directly read the coordinates in the drawing frame.

The 3D frame can be rotated by drawing with the mouse, zoomed by drawing while the Shift key is pressed, and shifted by drawing while the Strg key is pressed.

Autor vecteurs3dcompvues Jean-Marc Von Siebenthal, Ph D
I am a physic teatcher, trying to inoculate the pleasure to learn physic in a high school of Geneva, Switzerland.
You can visit the site I use with my students : "Physique et Graffiti" at
http://hypo.ge.ch/www/physic/
For any questions mail to : jean-marc.von-siebenthal@edu.ge.ch Extensions Dieter Roess Februar 2009

This simulation is part of

“Learning and Teaching Mathematics using Simulations

– Plus 2000 Examples from Physics”

ISBN 978-3-11-025005-3, Walter de Gruyter GmbH & Co. KG

 

Translations

Code	Language		Translator	Run

Credits

Dieter Roess - WEH- Foundation; Fremont Teng; Loo Kang Wee

1. Introduction:

This briefing document provides a review of the "Single Vector in 3D JavaScript Simulation Applet HTML5" interactive resource available on the Open Educational Resources / Open Source Physics @ Singapore website. This resource is designed for learning and teaching mathematics and physics concepts related to vectors in three dimensions. The document outlines the main features, functionalities, and pedagogical implications of this simulation applet.

2. Main Themes and Important Ideas/Facts:

The primary focus of the "Single Vector in 3D JavaScript Simulation Applet HTML5" is to provide an interactive and visual tool for understanding and manipulating single vectors in a three-dimensional Cartesian coordinate system. Key themes and important ideas presented by this resource include:

• Visualization of 3D Vectors: The core functionality allows users to see a vector represented as an arrow in a 3D space. This visual representation aids in understanding the concept of a vector having both magnitude and direction in three dimensions. As the description states, it offers a "Single vector in 3D view".
• Random Vector Generation: The applet features a "random vector button" which generates a vector with a random orientation starting from the origin. The endpoint of this vector has random integer coordinates (x, y, z) within a range of ∓ 5. The generation of the x-coordinate is explicitly defined as "x = integer(10*random( ) - 5)." This feature allows for quick exploration of various vectors.
• Manual Coordinate Input: Users can directly interact with the vector by editing the "number fields" that display the x, y, and z coordinates. These fields are editable, allowing users to input any rational number within the coordinate system's range. This facilitates precise exploration of specific vectors.
• Alternative 2D Drawing Input: The applet offers an alternative method to define the vector by allowing users to "draw the arrowhead in 2 dimensions with the mouse." This provides a more intuitive way to interact with the vector, particularly for visual learners.
• Coordinate System and Projections: A "transparent coordinate mesh forms the background of the vector," providing visual context within the ∓ 5 range on each axis. The applet also features a button "with/no xyz projections" to show or hide the projections of the vector onto the xy, yz, and xz coordinate planes. This is crucial for understanding the vector's components in each dimension.
• Multiple Viewing Perspectives: Five different "view" options are available through radio buttons, offering distinct projections of the 3D space. The description highlights that "the 2D projections are especially suited to directly read the coordinates in the drawing frame." This allows users to analyze the vector from different angles and understand its 2D components.
• Interactive 3D Manipulation: The 3D frame is interactive, allowing for "rotated by drawing with the mouse, zoomed by drawing while the Shift key is pressed, and shifted by drawing while the Strg key is pressed." These manipulation features enable a comprehensive exploration of the vector from various perspectives and distances.
• Integration into Webpages: The resource provides an "Embed this model in a webpage:" option with an iframe code. This allows educators and learners to easily integrate the interactive simulation into their own online learning materials.
• Attribution and Context: The applet clearly identifies the authors, Jean-Marc Von Siebenthal (a physics teacher), and Dieter Roess (for extensions). It also links to the author's website, "Physique et Graffiti," and provides an email address for questions. Furthermore, it contextualizes the simulation as part of the larger project "Learning and Teaching Mathematics using Simulations – Plus 2000 Examples from Physics."
• Instructions for Use: Clear instructions are provided for the "Control Panel," detailing the functionality of buttons like "Random Vector," the "Combo Box: View," the "Combo Box: Components" for manual input, the "XYZ Projection" toggle, the "Toggling Full Screen" option, and the "Reset Button."
• Connection to Learning Goals and Teaching: The resource includes sections for "Sample Learning Goals" and "For Teachers," indicating its intended pedagogical use. While the specific learning goals are not provided in the excerpt, their presence suggests the tool is designed to support specific educational objectives.
• Part of a Larger Collection: The applet is listed among a vast collection of other physics and mathematics simulations, highlighting the broader scope of the Open Educational Resources / Open Source Physics @ Singapore project. The extensive list includes simulations covering topics from magnetism and mechanics to waves and optics.

3. Pedagogical Implications:

This simulation applet offers significant pedagogical value for teaching and learning about vectors:

• Enhanced Visualization: The 3D visual representation can make the abstract concept of vectors more concrete and accessible to students, particularly those who are visual learners.
• Active Learning: The interactive features, such as generating random vectors, manually inputting coordinates, and manipulating the 3D view, encourage active exploration and experimentation, leading to deeper understanding.
• Conceptual Understanding: By observing the projections of the vector onto different planes and manipulating its components, students can develop a stronger intuitive understanding of vector components and their relationship to the overall vector.
• Flexibility and Adaptability: The ability to embed the simulation and the various viewing options make it adaptable to different teaching styles and learning environments.
• Connecting Math and Physics: The resource explicitly links mathematical concepts of vectors to physics, demonstrating their relevance in scientific contexts.

4. Noteworthy Features:

• The explicit mention of the coordinate generation code provides transparency about how the random vectors are created.
• The inclusion of author information and contact details fosters a sense of community and support for educators using the resource.
• The categorization under "Electricity and Magnetism" and "Magnetism" suggests potential applications of this basic vector visualization tool in these physics topics, even though the simulation itself is purely mathematical.
• The extensive list of related simulations indicates a rich ecosystem of interactive learning tools available on the platform.

5. Conclusion:

The "Single Vector in 3D JavaScript Simulation Applet HTML5" is a valuable open educational resource for visualizing and interacting with three-dimensional vectors. Its intuitive interface, multiple manipulation options, and clear instructions make it a useful tool for students learning about vectors in mathematics and physics. The ability to embed the simulation further enhances its utility for educators. The resource aligns with the broader goals of promoting active learning and conceptual understanding through interactive simulations.

 

Study Guide: Single Vector 3D JavaScript Simulation

Key Concepts

• Vectors: Mathematical objects possessing both magnitude and direction, often represented as arrows in space.
• 3D Space: A three-dimensional coordinate system defined by x, y, and z axes, allowing for the representation of objects and their positions in space.
• Origin: The point where the x, y, and z axes intersect in a 3D coordinate system, often denoted as (0, 0, 0).
• Coordinates (x, y, z): A set of three numbers that specify the position of a point in 3D space relative to the origin along the x, y, and z axes, respectively.
• Random Vector Generation: The process of creating a vector with randomly determined components (x, y, z) within a defined range.
• Vector Components: The scalar values (x, y, and z) that define the vector's extent along each of the coordinate axes.
• Projections: The shadows of the 3D vector cast onto the 2D coordinate planes (xy, yz, xz), visually representing the vector's components.
• User Interface (UI): The elements of the simulation that allow user interaction, such as buttons, number fields, and radio buttons.
• Interactivity: The ability of the user to manipulate and observe the simulation in real-time through actions like clicking, dragging, and inputting values.
• Coordinate Mesh: A grid displayed in the background of the 3D view to provide a visual reference for the coordinate system.
• Rational Numbers: Numbers that can be expressed as a fraction p/q, where p and q are integers and q is not zero.
• Integer: A whole number; can be positive, negative, or zero.

Quiz

1. Describe how a random vector is generated in the simulation. What is the range of the integer coordinates for the endpoint of this vector?
2. Explain the purpose of the editable number fields in the simulation. How can users interact with these fields to modify the vector?
3. What does the "with/no xyz projections" button control in the simulation? How do these projections help in understanding the vector?
4. List the five different "view" options provided by the radio buttons. How are the 2D projections particularly useful?
5. Describe the three ways a user can manipulate the 3D frame using the mouse. What keys, if any, are required for zooming and shifting?
6. Who are the authors credited for the development and extensions of this simulation? What are their affiliations or roles?
7. According to the "Instructions," what happens when a user clicks the "Random Vector" button multiple times?
8. Explain the function of the "Combo Box: View" in the control panel. What perspectives can be toggled using this feature?
9. How can a user input their own vector coordinates into the simulation, rather than using the random generation feature?
10. What is the purpose of the "Reset Button" in the simulation's control panel?

Quiz Answer Key

1. When the "random vector" button is activated, a vector arrow originating from the origin is generated with its endpoint having random integer coordinates (x, y, z). The range for each of these integer coordinates is -5 to +5.
2. The editable number fields display the current x, y, and z coordinates of the vector's endpoint. Users can click on these fields and enter any rational number to manually define the vector's components and change its orientation and magnitude.
3. The "with/no xyz projections" button toggles the visibility of the vector's projections onto the xy, yz, and xz coordinate planes. These projections visually break down the 3D vector into its 2D components, making it easier to read the x, y, and z values.
4. The five "view" options select different perspective projections of the 3D vector. The 2D projections (Planar YZ, Planar XZ, Planar XY) are especially useful because they align the view with one of the coordinate planes, allowing users to directly read the corresponding two coordinates in the drawing frame.
5. The 3D frame can be rotated by clicking and dragging the mouse. It can be zoomed in or out by clicking and dragging while holding the Shift key. The frame can be shifted (translated) by clicking and dragging while holding the Strg (Ctrl) key.
6. The original author is Jean-Marc Von Siebenthal, a physics teacher from Geneva, Switzerland. Dieter Roess provided extensions to the simulation in February 2009.
7. Clicking the "Random Vector" button repeatedly will generate a new vector with a different random orientation and integer coordinates within the specified range (-5 to +5) each time.
8. The "Combo Box: View" allows the user to select different perspectives of the 3D panel. This includes toggling between various planar (2D) views such as Planar YZ, Planar XZ, and Planar XY, as well as different 3D perspectives.
9. Users can input their own vector coordinates manually using the "Combo Box: Components." This likely refers to the editable number fields where the x, y, and z values can be directly entered.
10. The "Reset Button" in the simulation's control panel serves to return the simulation to its initial state, likely resetting the vector to a default value or clearing any user modifications to the view or components.

Essay Format Questions

1. Discuss the pedagogical benefits of using a 3D vector simulation like the one described in the source material for teaching and learning about vectors in physics or mathematics. Consider the different interactive features and how they might enhance student understanding.
2. Analyze the user interface of the "Single Vector in 3D JavaScript Simulation Applet HTML5." How effectively does it allow users to explore and manipulate 3D vectors? Suggest any potential improvements or additional features that could enhance its usability.
3. Compare and contrast the different methods available in the simulation for defining a vector (random generation, manual input, and potentially drawing in 2D). What are the advantages and disadvantages of each method for different learning objectives?
4. Explain how the "with/no xyz projections" feature and the different "view" options contribute to a student's understanding of the three-dimensional nature of a vector and its components. How do these visual aids bridge the gap between abstract concepts and concrete representations?
5. Based on the information provided, how does this simulation align with the principles of open educational resources and the goals of "Learning and Teaching Mathematics using Simulations – Plus 2000 Examples from Physics"? Discuss the accessibility, adaptability, and potential impact of such resources in education.

Glossary of Key Terms

• Applet: A small application, often written in Java or JavaScript, that runs within another application, typically a web browser.
• Embed: To integrate content from one source (like the simulation) into another (like a webpage) so that it appears as part of the destination content.
• HTML5: The latest evolution of the standard markup language for creating web pages and web applications, enabling interactive elements and multimedia without the need for plugins.
• JavaScript: A high-level, often just-in-time compiled programming language that conforms to the ECMAScript specification. It is commonly used to make web pages interactive.
• Open Educational Resources (OER): Teaching, learning, and research materials that are in the public domain or released with an open license, permitting no-cost access, use, adaptation, and redistribution by others with no or limited restrictions.
• Simulation: A computer program that models a real or imagined system to allow for experimentation and observation of its behavior over time or under different conditions.
• Vector Arrow: A graphical representation of a vector, where the length of the arrow corresponds to the magnitude of the vector, and the direction of the arrow indicates the vector's direction.
• Zoom: To adjust the viewing scale, making objects appear larger (zoom in) or smaller (zoom out).
• Shift (Pan): To move the viewpoint or the entire scene horizontally or vertically without changing the magnification.
• Rotate: To turn the viewpoint or the object around a central axis.

Sample Learning Goals

[text]

For Teachers

Single Vector in 3D JavaScript Simulation Applet HTML5

Instructions

Control Panel

Random Vector

Combo Box: View

Combo Box: Components

XYZ Projection

Toggling Full Screen

Reset Button

Research

[text]

Video

[text]

 Version:

Other Resources

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Frequently Asked Questions: Single Vector 3D JavaScript Simulation Applet

1. What is the primary purpose of the Single Vector in 3D JavaScript Simulation Applet?

The primary purpose of this applet is to allow users to visualize and manipulate a single vector in a three-dimensional space. It serves as an interactive tool for learning and teaching about vectors, particularly their representation and components in 3D.

2. How can a user interact with the random vector generation feature?

By clicking the "random vector" button, the applet generates a vector that originates from the origin of the 3D coordinate system. The endpoint of this vector has random integer coordinates along the x, y, and z axes, within a range of -5 to +5. Each subsequent click produces a new random vector.

3. What options are available for manually defining a vector within the simulation?

Users can manually define a vector by entering rational numbers into the three editable "number fields" corresponding to the x, y, and z coordinates. Additionally, the arrowhead of the vector can be drawn in a 2D plane using the mouse, providing an alternative way to input vector components.

4. How can the perspective and orientation of the 3D vector visualization be adjusted?

The 3D frame can be manipulated using mouse interactions. Users can rotate the view by dragging the mouse, zoom in and out by dragging while holding the Shift key, and shift the entire coordinate system by dragging while holding the Strg (Ctrl) key. Furthermore, five different "view" radio buttons offer distinct projections, including 2D views that facilitate direct reading of the coordinates.

5. What are "xyz projections" and how can they be controlled?

"xyz projections" refer to the projections of the 3D vector onto the xy, xz, and yz coordinate planes. A button labeled "with/no xyz projections" allows users to toggle the visibility of these projections, aiding in understanding the vector's components in each plane.

6. Is it possible to view the vector in a two-dimensional plane, and how is this helpful?

Yes, the applet offers several "2D" projections through the "view" radio buttons. These 2D views are specifically designed to make it easier to directly read the x, y, and z coordinates of the vector's endpoint within the drawing frame, simplifying the understanding of individual components.

7. Can this simulation be integrated into other web pages or learning platforms?

Yes, the applet can be easily embedded into other web pages using the provided <iframe> HTML code. This allows educators and learners to incorporate the interactive vector visualization tool into their online resources and learning environments.

8. Who developed this simulation and where can more information or assistance be found?

This "Single Vector in 3D JavaScript Simulation Applet HTML5" was primarily authored by Dieter Roess. The simulation is part of the "Learning and Teaching Mathematics using Simulations – Plus 2000 Examples from Physics" project.