Lesson 30 – Intersection of Lines

1. Lesson 30 – Intersection of Lines September 10, 2013 Fernando Morales

2. Learning Goals • Recognize geometrically intersection of lines in two-space and three-space • Solve for the point of intersection of lines in various different ways • Derive the formula for measuring the shortest distance between skew lines

3. Peer Instruction • Given a system of linear equations in two-space, how manytypes of solutions are possible? Explain. [K, C] • The direction vectors of two lines in three-space are not parallel. Does this indicate that the lines intersect? Explain. [A, C] • How can you tell if two lines are in three-space are skew? Use examples to explain. [A, C]

4. Linear systems in 2D (p.463) • Two Distinct Lines • Unique pair of numbers • Exactly one solution or intersection

5. Linear systems in 2D (p.463) • Two Coincident Lines • 0x = 0 or 0y = 0 • Infinite number of solutions or intersections

6. Linear systems in 2D (p.463) • Two distinct but parallel lines • 0x = 2 or 0y = 1 • No solutions

7. Linear systems in 3D (p.465)

8. Linear systems in 3D (p.465)

13. Skew Lines • Direction Vectors are non-parallel • No intersection = No solution

14. The distance between two skew lines (p. 468) • Shortest Distance • Common Perpendicular • Use Projection

15. Required Before Next Class • Section 8.4 # 1, 2, 4ab, 5ab, 6ab, 8, 10