1. L ESSON 30 – I NTERSECTION OF L INES September 10, 2013 Fernando Morales

2. L EARNING G OALS 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. P EER I NSTRUCTION Given a system of linear equations in two-space, how many types 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. L INEAR SYSTEMS IN 2D ( P.463) Two Distinct Lines Unique pair of numbers Exactly one solution or intersection

5. L INEAR SYSTEMS IN 2D ( P.463) Two Coincident Lines 0 x = 0 or 0 y = 0 Infinite number of solutions or intersections

6. L INEAR SYSTEMS IN 2D ( P.463) Two distinct but parallel lines 0 x = 2 or 0 y = 1 No solutions

7. L INEAR SYSTEMS IN 3D ( P.465)

13. S KEW L INES Direction Vectors are non-parallel No intersection = No solution

14. T HE DISTANCE BETWEEN TWO SKEW LINES ( P. 468) Shortest Distance Common Perpendicular Use Projection

15. R EQUIRED B EFORE N EXT C LASS Section 8.4 # 1, 2, 4ab, 5ab, 6ab, 8, 10