Examples and practice
Vectors: planes, normals and distances
Back to lessonPractice section 1 · Questions 1–6
Build a parametric plane from lines or points · Use a point and a normal to write a plane · +4 more
Practice section 2 · Questions 7–12
Find the acute angle between a line and a plane · Check a point by substituting into a plane · +4 more
Practice section 3 · Questions 13–18
Use two plane normals and their common base point · Measure the acute angle using two plane normals · +4 more
- Use two plane normals and their common base point
- Measure the acute angle using two plane normals
- Cut a cuboid and check where a perpendicular drill exits
- Three forms of a plane in four settings
- Classify a line relative to a plane before solving
- Use a plane normal to measure distance and construct a perpendicular plane
Practice section 4 · Questions 19–24
Drop a normal from a point and reflect through its foot · Reflect a line using its fixed intersection and one reflected point · +4 more
- Drop a normal from a point and reflect through its foot
- Reflect a line using its fixed intersection and one reflected point
- Find a common line and use normals for the acute plane angle
- Equate absolute normal distances to two intersecting planes
- Separate a unique triple intersection from a common line
- Interpret a plane equation and derive the line-intersection parameter
Practice section 5 · Questions 25–30
Project a pyramid shadow under two different lighting models · Build an intersection line and a perpendicular plane · +4 more
- Project a pyramid shadow under two different lighting models
- Build an intersection line and a perpendicular plane
- Use prism geometry to choose line and plane directions
- Find a line-plane angle and reflect a point
- Separate plane angles, intersections and orthogonal directions
- Construct a plane parallel to a line and measure their separation
Practice section 6 · Questions 31–36
Use normals for parallel planes and lines inside a plane · Recover plane constants from an intersection line · +4 more
- Use normals for parallel planes and lines inside a plane
- Recover plane constants from an intersection line
- Transform a plane after finding intersections and parallel offsets
- Reflect a plane by retaining its intersection and reflecting one point
- Construct a line equidistant from two perpendicular planes
- Use line and plane distances to determine a parallel plane
Practice section 7 · Questions 37–40
Reflect a light ray using the plane normal · Find the locus of a fixed-ratio point between a line and a plane · +2 more