Question

Two distinct nonparallel planes intersect in a line. Outline a procedure for finding the equation of the line of intersection.

Short answer

Find the normal vectors, the direction vector, the point of intersection and the line of intersection.

Step-by-step solution

Given information

Two distinct non-parallel planes intersecting in a line.

Calculation

The goal is to lay out the steps for determining the equation of the line of intersection. The steps for determining the equation of the line of intersection are as follows.

• First find the normal vectors ${\mathbf{N}}_1$ and ${\mathbf{N}}_2$ of the two planes.

$\mathbf{d}={\mathbf{N}}_1\times {\mathbf{N}}_2$

• Find the point of intersection $(\alpha ,\beta ,0)$of two planes by setting $z=0$
• The line of intersection is given by $\mathbf{r}\left(t\right)=⟨\alpha +at,\beta +bt,ct⟩$