Calculus › Section L · Vectors and the geometry of space › Topic L.5
Lines and planes in space
In the plane, a slope pins down a line. In space there is no single slope, so lines and planes are described by vectors instead: a line follows a direction vector, and a plane stands perpendicular to a normal vector.
In this topic
- From slope to direction vectors
- Parametric equations of a line
- Symmetric equations
- Worked example: a line through two points
- Planes from a normal vector
- Worked example: a plane through three points
- How planes meet
- Distances to planes and lines
- Worked example: how far is the hiker from the trail?
- Common mistakes to avoid
- Key takeaways
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Standards: Beyond AP