Sometimes we want to calculate the line at which two planes intersect each other. We can accomplish this with a system of equations to determine where these two planes intersect. Note that this will result in a system with parameters from which we can determine parametric equations from.

# Lines of Intersection Between Planes

Let’s hypothetically say that we want to find the equation of the line of intersection between the following lines $L_1$ and $L_2$:

(1)

We will begin by first setting up a system of linear equations. Note that we have more variables (3) than the number of equations (2), so there will be a column of zeroes after we convert the matrix of lines $L_1$ and $L_2$ into reduced row echelon form. The following matrix represents our two lines: $\begin{bmatrix}2 & -1 & -4 & -2 \\ -3& 2 & -1 & -2 \end{bmatrix}$.

We will thus convert this matrix intro reduced row echelon form by Gauss-Jordan Elimination:

(2)

(3)

(4)

(5)

(6)

We now have the system in reduced row echelon form. We can see that we have a free parameter for $z$, so let’s parameterize this variable. Let $z = t$ for $(-\infty . Therefore, we can determine the equation of the line as a set of parameterized equations:

(7)

### Related post:

- Grade Nine learners taught mathematics skills – Tembisan
- A Library Browse Leads Math’s Bill Dunham to Question the Origins of The Möbius Function – Bryn Mawr Now
- Year 5 and 6 students to sit competition this Wednesday – Great Lakes Advocate
- USC student wins silver medal in China math contest – SunStar Philippines
- CBSE Exam 2020: Two separate examinations to be conducted for Class 10 Mathematics – Jagran Josh
- Concepts incomplete, problems unsolvable in math textbooks – Times of India
- Education Ministry to Host Tertiary and Employment Fairs – Government of Jamaica, Jamaica Information Service
- Vogue’s Edwina McCann and Westpac’s Anastasia Cammaroto on how they inspire women to pursue STEM – Vogue Australia
- Jonee Wilson, Temple Walkowiak to Measure High-Quality Instructional Practices to Support Marginalized Students in Rigorous Mathematics through NSF Grant – NC State College of Education
- Australian Conference on Science and Mathematics Education – Australian Academy of Science