Cross Product Demo
Enter in values for the components of and Click the button to see a demonstration of one method of how to calculate the dot product. Step 1: Write each vector in a column twice, lining up their components. Step 2: Remove the topmost and bottom most element from each column. Step 3: Draw your arrows from left to right down then up for each number in the left column Step 4: Record the products that the arrows designate, subtracting the "up" products from the "down ones for each pair. Note that each pair of crossed arrows is used to find one component of the resultant vector. Step 5: Simplify each component of the resultant vector. When the demo is finished, click the second button to see an alternate method. Step 1: Write each vector as a row, one under the other Step 2: Cover the x components and calculate the product "down-right" subtract the product "up right" Step 3: Cover the y components and calculate the product "down-left" subtract the product "up left" NOTE this is backwards compared to other steps Step 4: Cover the z components and calculate the product "down-right" subtract the product "up right" Step 5: Simplify each component of the resultant vector.
What do you notice about the components being used to calculate each part of the resultant vector? Which components are being used from the original vectors to calculate the x-component? The y? The z? Although it doesn't look like it because it is drawn in 2 dimensions, the resultant vector is perpendicular (or normal) to both of the original vectors. Can you think of a way to check this property? What would happen if the order of the multiplication were reversed (ie vs. )? What would change? What does this tell us about the nature of the cross product?