Math Teacher Master Class: Pre-Calculus Vectors

The focus of this Master Class is to explore vectors, their properties, and their formulas.  We will derive the formula for the angle between vectors from the Law of Cosines, and discuss the importance of the dot product.  Then we will discuss the cross product and see the orthogonal vector it creates.

Vectors

Explore the applet to see how vectors affect the cross product in real time.

https://mathinsight.org/applet/cross_product

What happens when the two vectors make an angle close to zero degrees?

What happens when the two vectors make an angle close to 90 degrees?

What about when the angle between them makes an angle close to 180 degrees?

Do you see the relationship between the magnitude of the cross product and the area of the parallelogram formed by the two vectors?

Next, consider the applet below.

You can select vectors specifically and see their cross product in real time.

Source: https://www.geogebra.org/material/show/id/pcMtbdq8