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EXAMPLES FOR EXAM I Sections 11.1 - 11.4

 

If it is not already on your hard drive, you will need to download the free DPGraph Viewer to view some of the pictures linked to on this page.   QuickTime 7 free download.

 

Here is a short Powerpoint presentation on operations and definitions for vectors in space.  The operations and definitions would be similar for vectors in the plane.

Here is a Maple Worksheet with dot product and cross product examples.

 

Example--Vector Addition, Vector Properties

 

 

Vector Equilibrium Example

A 100-pound collar (the green rectangle) slides on a frictionless vertical rod.  Find the distance y (the distance from A to B) for which the system is in equilibrium if the collar is attached by a pulley to a 120 pound counterweight.

  

y is the distance from A to B.

 

 

Vector Force Example--Tugboats

Click on the picture below to see an animation.
 

 

 

Distance Between Points in Space

Find the distance between points P and Q.

Click on the picture at the right to animate.

 

 

 

Finding The Equation Of A Sphere

DPGraphPicture    Transparent Picture of the Sphere with Points P and Q

Finding The Center And Radius Of A Sphere

DPGraphPicture     Transparent Picture of the Sphere with Center

(x - 1)2 + y2 + (z - 1)2 = 27

 

 

Direction Cosines

 

 

 

Direction Cosines

 

 

Projections and Vector Components

 

The picture below represents the vectors in the example at the left with the colors corresponding to vectors as indicated in the picture above.  Click on the picture below to see an animation.

 

 

 

Work Example

Click here to see the answer and a related animation.

 
       

Click here or on the picture above to see an animation.  Click here for an animation without scales.

 

 

Work Example

Click on the picture at the right to animate the red force vector.

 

 

Example--Volume Of A Parallelepiped

DPGraphPicture

Click here to see an animation of the three vectors in standard position.

 

 

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        Lane Vosbury, Mathematics, Seminole State College   email:  vosburyl@seminolestate.edu

        This page was last updated on 08/21/14          Copyright 2002          webstats