Skip to main content
Search IntMath
Close

450+ Math Lessons written by Math Professors and Teachers

5 Million+ Students Helped Each Year

1200+ Articles Written by Math Educators and Enthusiasts

Simplifying and Teaching Math for Over 23 Years

Tips, tricks, lessons, and tutoring to help reduce test anxiety and move to the top of the class.

Intersection of 3 planes at a point: 3D interactive graph

By Murray Bourne, 28 Jun 2016

I recently developed an interactive 3D planes app that demonstrates the concept of the solution of a system of 3 equations in 3 unknowns which is represented graphically as the intersection of 3 planes at a point.

We learn to use determinants and matrices to solve such systems, but it's not often clear what it means in a geometric sense. Most of us struggle to conceive of 3D mathematical objects.

Technology to the rescue.

The new app allows you to explore the concepts of solving 3 equations by allowing you to see one plane at a time, two at a time, or all three, and the intersection point. You can also rotate it around to see it from different directions, and zoom in or out.

Here's a screen shot:

3 intersecting planes meeting at a point
Three planes intersecting at a point

On the other hand, solving systems of 2 equations in 2 unknowns is represented by the intersection of 2 lines (or curves), which is relatively more straightforward.

The link again:

Systems of 3×3 Equations interactive applet

See the 1 Comment below.

One Comment on “Intersection of 3 planes at a point: 3D interactive graph”

  1. Leesa Johnson says:

    Nice explanation for me to understand the interaction of 3d planes at a point using graphical representation and also useful for the math students.

Leave a comment




Comment Preview

HTML: You can use simple tags like <b>, <a href="...">, etc.

To enter math, you can can either:

  1. Use simple calculator-like input in the following format (surround your math in backticks, or qq on tablet or phone):
    `a^2 = sqrt(b^2 + c^2)`
    (See more on ASCIIMath syntax); or
  2. Use simple LaTeX in the following format. Surround your math with \( and \).
    \( \int g dx = \sqrt{\frac{a}{b}} \)
    (This is standard simple LaTeX.)

NOTE: You can mix both types of math entry in your comment.

top

Tips, tricks, lessons, and tutoring to help reduce test anxiety and move to the top of the class.