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Vectors and Planes

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Examples, solutions, videos, worksheets, and activities to help PreCalculus students learn about vector equations for planes.

Introduction to Planes
When introduced to the 3D coordinate system we are introduced to the concept of math planes, and vector equations for planes. Math planes are used frequently with vectors, when calculating normal vectors to planes or when finding the angle between two planes. It is simpler to find the equations of math planes that is formed by two axes, or a plane that is parallel to one.
Determining the equation for a plane in R3 using a point on the plane and a normal vector
Vectors and Planes
An important calculation when dealing with vectors and planes, is being able to find a vector normal to a plane through a specific point. There are methods for finding the normal or perpendicular vector to a plane and finding the plane to which a vector is normal. This relationship between vectors and planes is important and is used in the calculation of the angle between planes.
Figuring out a normal vector to a plane from its equation

Intersection of a Line and a Plane
The Angle Between Planes
We can use knowledge of how to find the angle between vectors to help us find the angle between planes. We can use the dot product to find the angle between planes, or determine whether or not the planes are perpendicular or parallel. In order to find the angle between planes we must understand finding vectors normal to planes.
This video explains how to determine the angle between two planes.

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