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Vectors in Three Dimensions

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Examples, solutions, videos, worksheets, games, and activities 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 xyz 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 Three Space
This video lesson shows how to do the following in three space:
- graph in three dimensional space
- find the components of a vector between 2 specific points
- find the magnitude of a vector
- add, subtract and perform scalar multiplication on vectors
- determine if two vectors are parallel (or collinear)
- find an orthogonal (normal) vector to a specific vector
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.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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