Vectors in 3D
Explaining all the concepts needed in 3D vectors to aid in visualisation and problem solving. Questions are taken from Haese and Harris Higher Level Mathematics Textbook 3rd Edition (2012)
Inhaltsverzeichnis
- Lines in 3D
- Equation of a Line in 3D
- Intersections
- Angles
- Distances
- Applications
- Planes
- Equations of Planes
- Lines and Planes
- Distances
- Angles
- Problem Solving
- Intersecting Planes
Equation of a Line in 3D
Instructions
Manipulate the Geogebra applet to help visualise the problem you are solving.[br][br]For this example you can use the sliders to edit the components of each point and vector.
What is the minimum amount of information needed to find the equation of a line in 3D?
Equations of Planes
Instructions
Adjust and manipulate the applet to help solve the problems.
The Normal
Imagine a plane, like the floor or a table. Imagine place a pen perpendicular to this plane. Notice that wherever you move the pen on the table, the pen is always in the same direction. Therefore, this perpendicular vector is the same at any point on the plane, this is call the [b]normal vector[/b] to the plane.
Finding the Equation of the Plane
Consider the image below to find the equation of the plane. [br]You are given a [b]normal vector[/b], a specific point [b][math]A[/math][/b] and a general point [math]R\left(x,y,z\right)[/math].[br][br](Note: the normal is perpendicular to the plane)
What information is needed in order to find the equation of the plane?
How do you find the Cartesian Equation of a Plane
Use the geogebra file below to help with this task. There are ready made points and vectors, which you can edit to fit the information in the question.[br]For part c) make sure you show the line and then the plane you have found.