1. Intersections of Lines in 2 Space Three Cases: 1) 2) 3)

2. Examples: 1) x – 2y = 5 x + 4y = 8 2) -15x + 18y = -8 5x – 6y = 3 3) 4x – 3y = 1 8x – 6y = 2

3. 4) (x,y) = (-3,5) + s(4,-9) (x,y) = (2,-1) + t(-4,9)

4. 5) (x,y) = (1,0) + s(-3,4) (x,y) = (-3,6) + t(5,2)

5. Intersection of Lines in Three Space 4 Cases: 1) 2) 3) 4)

6. Examples: 1) (x,y,z) = (4,2,-2) + s(-3,4,1) (x,y,z) = (0,3,1) + t(-3,4,1)

7. 2) (x,y,z) = (7,2,-6) + s(2,1,-3) (x,y,z) = (3,9,13) + t(1,5,5)

8. 3) (x,y,z) = (5,-4,-2) + s(1,2,3) (x,y,z) = (2,0,1) + t(2,-1,-1)

9. The Distance between 2 Skew Lines

10. Example: Find the distance between the two lines (x,y,z) = (5,-4,-2) + s(1,2,3) (x,y,z) = (2,0,1) + t(2,-1,1) HW p.156 #1,2,4,5,6, 9abcdf,12ab