Vectors in Three Dimensions

Videos, worksheets, games and acivities to help PreCalculus students learn about three dimensional vectors.



Introduction to the 3D Coordinate System :
With vectors, we begin to work more with the 3D coordinate system. In the 3D coordinate system there is a third axis, and in equations there is a third variable. We will work with vectors in the 3D coordinate system and learn how to interpret the coordinates an of a vector in the 3D coordinate system. With the introduction to the 3D coordinate system, we also encounter other vector operations, lines and planes.

This video introduces the xyx coordinate system and explains how to plot point in R3. 



Vector Length in the Third Dimension
Find the length of a 3d Cartesian vector



Vectors in 3 dimensions
Vectors with 3 components can be drawn in 3 dimensions. We also learn how to calculate the length of a vector in 3 dimensions



Vector Operations in 3D :
Although they are similar to 2D vector operations, it is good to get practice doing 3D vector operations. 3D vector operations include addition and scalar multiplication, the dot product and the calculation of magnitude. The biggest difference in these 3D vector operations is an added step of computation. With 3D vector operations we can do computation such as find the angle between vectors in space.




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