Unit 6 · 5 lessons
Lines & Planes
Describe lines and planes with scalar, vector and parametric equations, sort out how lines and planes meet in 3-space, solve systems of three equations as three planes, and measure the shortest distances between them.
- 49 practice questions
- 38 flashcards
- 2 interactive lessons
Lessons
- 1Lines in 2-SpaceOne line, three descriptions: the scalar equation Ax + By + C = 0 with its normal vector, the vector equation r = r₀ + tm, and parametric equations. Convert between them and decide when two lines meet.9 questions
- 2Lines in 3-SpaceWhy a line in 3-space has no single scalar equation, how to write its vector, parametric and symmetric equations from a point and a direction or from two points, and how to tell intersecting, parallel, coincident and skew lines apart.10 questions
- 3Planes: Normals and EquationsA single linear equation in x, y and z is a plane. Use its normal vector to write the scalar equation Ax + By + Cz + D = 0, use two direction vectors for the vector and parametric equations, and convert between the forms.Interactive10 questions
- 4Intersections of Lines and PlanesWhere a line meets a plane, where two planes meet, and where three planes meet. Solve each case algebraically, use the triple product test, and read every algebraic outcome (one solution, infinitely many, none) as a picture.Interactive10 questions
- 5Distances in 3-SpaceShortest distances are measured along a perpendicular. Use the scalar projection onto a normal for a point and a plane (and parallel planes), the cross product for a point and a line, and both together for two skew lines.10 questions