# Lecture 4: Square systems and equations of planes.

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Lesson Summary:

In Lecture 4, you will learn how to find equations for planes and determine if and where planes intersect each other using matrices. Equations of planes will be expressed in the form of AX + BY + CZ = D, where A, B, C, and D are numbers. The coefficients of X, Y, and Z give us the normal vector to the plane. By applying these concepts to linear systems, you will learn how to find the solution to a system of equations and what can happen when there is no solution, a line solution, or a plane solution.

Lesson Description:

Learn how to find equations for planes and determine if and where planes intersect each other using matrices.

Denis Auroux. 18.02 Multivariable Calculus, Fall 2007. (Massachusetts Institute of Technology: MIT OpenCourseWare). http://ocw.mit.edu (Accessed March 15, 2009). License: Creative Commons Attribution-Noncommercial-Share Alike.

Questions answered by this video:
• What are square systems?
• How do you write an equation of a plane through a point given a normal vector??
• How can you determine if two vectors are parallel or perpendicular?
• How can you determine if a vector is parallel or perpendicular to a plane?
• How can you solve a 3x3 linear system?
• How can you find where three planes intersect?
• How do you find the inverse of a matrix?
• When does a matrix have an inverse?
• What are square systems?
• How do you write an equation of a plane through a point given a normal vector??
• How can you determine if two vectors are parallel or perpendicular?
• How can you determine if a vector is parallel or perpendicular to a plane?
• How can you solve a 3x3 linear system?
• How can you find where three planes intersect?
• How do you find the inverse of a matrix?
• When does a matrix have an inverse?
• #### Staff Review

• Currently 4.0/5 Stars.
This video explains some very good examples of finding equations for planes given a point and a normal vector. This is a very practical, useful lecture. Also, you will learn how to find where planes and vectors intersect as well as where two or three planes intersect.