Math Analysis Cross Product Online Lesson

Do the following in order to learn about the cross product of two vectors and some of its applications!

1)

Watch the following video on how to calculate a cross product.

How to Find a Cross Product


2)

Try the following examples of finding the cross product.


 

Solutions

 

3)

Watch this video of a physics view of the cross product and a better explanation of the right-hand rule.

Another Explanation of the Cross Product

 

4)

The magnitude of the cross product of two vectors can be used to find the area of a parallelogram. Check out this Google Presentation demonstrating this idea.

 

5)

The dot product of a vector and the cross product of two other vectors is called the scalar triple product of all three vectors.  Watch this video for more explanation:

Scalar Triple Product

*A parallelepiped is a 3-D shape made up of 6 parallelograms!

 

6)

If you find that the volume of a parallelepiped is equal to 0, the 3 vectors that make up the adjacent edges all lie in the same plane (the figure is not 3 dimensional).  Try the following example:

Ex: Use the scalar triple product to show that the vectors a = <1, 4, -7>,                b = <2, -1, 4> and c = <0, -9, 18> are coplanar.

Solution

 

4)

One real world application of the cross product of two vectors is finding torque vectors and the magnitude of the torque vector.  Watch this example of finding a torque vector given a force and radial distance from the center of rotation.

Cross Product and Torque

 

5)

Try the following examples:

Ex 1:  A bolt is tightened by applying a 40N force to a 0.25m wrench as shown.  Find the magnitude of the torque about the center of the bolt.

 

 

 

 

Ex2: A bicycle pedal is pushed by a foot with a 60 N force as shown.  The shaft of the pedal is 18 cm. long.  Find the magnitude of the torque about P.

 

Solutions

 

 

 6)

Hooray! You have finished the online lesson focusing on cross product! You now get to receive your homework assign.  Hip-Hip-Hooray!  Your homework assignment is:

Section 12.4 Pg. 823 - 824 3, 7a, 10, 15, 17, 21, 23a, 31, 35.

This assignment will be due on Friday!  Oh and we have a quiz on 12.1 - 12.3 tomorrow!