Cross Product Applications

Click on a vector to show it's components. Drag each of the three components to the desired values. If you wish to see how those points make up the vector, click the "Show/Hide Construction Lines" button. When you are finished selecting values for all three vectors, click the "Hide Construction Points" button. To Show or Hide the Parallelopiped based on vectors , , and click the appropriate button. With the Parallelopiped showing, click the "Find Volume Button" to start the demonstration that defines the formula for the volume of the parallelopiped. Read each part then click next. When finished you can experiment with values to see how they affect the volume. Hold the shift key and use the mouse scroll wheel to zoom in or out.
What is a parallelopiped? How do you find the volume of one? Why might a parallelopiped look bigger on the isometric representation, but have a smaller volume? What concepts are needed to understand the formula for finding the volume of a parallelopiped?