Lines & Planes in 3D-Space: Definition, Formula & Examples


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Determine the vector equation of a line that passes through the points A (2 , -3 , 4) and B (5 , 2 , -1)

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1. Determine the equation of the plane that contains the following points: A (2, 1, 3), B (-1, -2, 4) and C (4, 2, 1)

2. Determine the equation of the line which contains the point P (2,3) and is parallel to the vector v = (3,1).

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About This Quiz and Worksheet

In this quiz and worksheet combo, you are looking at the use of lines and planes in 3-space. Questions ask you to determine a vector equation of a line passing through a pair of points, along with the elements needed to determine a plane.

Quiz and Worksheet Goals

The questions in this quiz are designed to check your knowledge of the following ideas:

  • Finding the equation of a plane containing three points
  • Determining the equation of a line containing a point and a parallel vector
  • Finding an equation for a plane containing a point and a perpendicular vector
  • How to determine a plane

Skills Practiced

  • Knowledge application - use what you know to answer questions about finding a vector
  • Information recall - remember what you have learned about finding parallel and perpendicular planes
  • Defining key concepts - ensure that you can name what is needed to determine a plane

Additional Learning

To find out more about the topics mentioned here, go to the lesson titled Lines & Planes in 3-Space: Definition, Formula & Examples. Utilizing this lesson shows you the other subject material listed here:

  • Cross products
  • General equations
  • Additional examples of equations