3.2 Addition of Vectors
Addition of Vectors in Three Dimensions
Instructions:
Click on the "Start Simulation" button to start the applet. You are advised to try the two-dimensional version before starting this one.   When you position your mouse cursor over the applet a vector joining the origin of coordinates to the cursor position appears.  Initially the vector is on the x,y plane.  You can change on this vector by moving the mouse around.  You can set the value of the vector by just clicking the left mouse button.  To give the vector a non-zero z component, you need to click and drag the mouse either up or down.  The x, y, and z components of the vector are displayed in the boxes on top. Once the first vector is selected, the applet's focus changes to the second vector. You can select the second vector by following the same method used in selecting the first.  Immediately after selecting the second vector, the applet performs an animation illustrating  the addition of both vectors.  All vector components are shown at the upper left corner.  You can add labels to the axis by selecting the "label" checkbox. You can change the viewing perspective of the graph by positioning your mouse over the graph, pressing the right mouse key (Windows) then dragging.  If you are using a Macintosh computer, you need to press the command (apple) key and the mouse button together to get the same effect.

Navigation: You can come back to this window by pressing the "Close Simulation" button on the bottom frame of the utility.  

start.gif (693 bytes)

Explanation:
This utility illustrates the graphical and analytical methods used to add three-dimensional vectors. The method is the same as the 2-d case illustrated in sections 3.2 and 3.3 of the book.  First, each vector is represented by its components.  As shown in figure 3.16, the vectors have three components. The sum is performed by adding the components as shown for two dimensions in examples 3.3 and 3.4.  The animation illustrates the graphical method used in adding vectors as discussed in section 3.2 for two dimensions.
 
Source:
Fu-Kwun Hwang

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