Vectors
This is a project for the lecture GeoGebra at Johannes Kepler University Linz. Lecture plan (for teachers): [url]https://www.geogebra.org/m/PJXudjhk[/url]
Table of Contents
- Basics - What is a vector?
- Explanation: What is a vector?
- A -> B
- Game: Setting up vectors
- Magnitude
- Direction
- Addition of vectors
- Graphical and algebraic addition
- Game: Resulting force
Explanation: What is a vector?
A vector has a direction and a magnitude. [br]Usually you draw them as arrows and write them as a small letter with an arrow on top ([math]\text{\vec{a}}[/math]).[br]To tell somebody how far and in which direction the vector points you write the x-component and the y-component in brackets.[br][math]\text{\vec{a}}[/math]=[math]\binom{x}{y}[/math][br]Excersice: Move the slider and look at the vector and the graphics. [br] If you think you know the answer to the vector, you can check it anytime.
Graphical and algebraic addition
We add vectors together by putting them head to tail.[br]As the addition is commutative it doesn't matter if we add [math]\text{\vec{a}}[/math]+[math]\text{\vec{b}}[/math] or [math]\text{\vec{b}}[/math]+[math]\text{\vec{a}}[/math].[br]In absolute terms, we add them together by sum up the components.[br][math]\text{\vec{a}}+\text{\vec{b}}=\binom{a_x}{a_y}+\binom{b_x}{b_y}=\binom{a_x+b_x}{a_y+b_y}=\binom{c_x}{c_y}=\text{\vec{c}}[/math]