More Lessons for PreCalculus
Examples, solutions, videos, worksheets, games and activities to help PreCalculus students learn about lines in the three dimensions coordinate system.
Lines in 3D
In the 3D coordinate system, lines can be described using vector equations or parametric equations. Lines in 3D have equations similar to lines in 2D, and can be found given two points on the line. In order to understand lines in 3D, one should understand how to parameterize a line in 2D and write the vector equation of a line. Perpendicular, parallel and skew lines are important cases that arise from lines in 3D.
3D equations of lines and planes
1. Equation of a 2D line in vector, parametric and symmetric forms.
2. Equation of a 3D line in vector, parametric and symmetric forms.
3. Equation of a plane in vector (passing mention) and Cartesian form.
4. Three methods for finding the line of intersection of two planes.
Including examples in all 4 parts, and a quick method for obtaining the cross product.
Parallel and Skew Lines in Space
With the introduction of the 3D coordinate system we find the concepts of skew, perpendicular and parallel lines in space. Skew lines are new, and are lines that are not parallel, yet never intersect. Perpendicular and parallel lines in space are very similar to those in 2D and finding if lines are perpendicular or parallel in space requires an understanding of the equations of lines in 3D.
Deciding if Lines Coincide, Are Skew, Are Parallel or Intersect in 3D.
Describe two lines in 3space using parametric equations. How to decide if they coincide, are parallel, are skew or if they intersect in exactly one point.
Determine if two 3D lines are parallel, intersecting, or skew
Deciding if Lines Coincide, Are Skew, Are Parallel or Intersect in 3D
This video describes two lines in 3space using parametric equations. We have to decide if they coincide, are parallel, are skew or if they intersect in exactly one point.
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