AAHL 3.18.2 Intersection between two planes

The video explains how to find the intersection of two planes, which typically forms a straight line. It discusses two methods: using a calculator to solve a system of linear equations and a manual approach that involves eliminating variables and introducing a parameter.

Key points include:

• The intersection can be represented in parametric form using a parameter $t$.
• The direction of the line of intersection can be determined using the cross product of the normals of the two planes.
• A practical example is provided, demonstrating how to derive the vector equation of the line of intersection, which can be expressed as: $\mathbf{r}(t)=\left(\begin{array}{c}{x}_0\\ y_0\\ z_0\end{array}\right)+t(\begin{array}{c}\end{array}$ where is a point on the line and is the direction vector.