1. Vector equation of lines (recap) Find a vector equation of the line through the points ( 2, 5 ) and ( 4, 9). Find a vector equation of the line parallel to the x-axis through the point ( 6, 3) Find a vector equation of the line parallel to i - 4j through the origin

2. Vectors lesson 3 Vectors in 3D i, j, k Vector equation of a line Intersection of two lines Practice questions

3. Vectors in 3D The axis below are said to be “right-handed”: if the outstretched index finger of your right hand points in the x-direction, and you bend your middle finger to point in the y direction, then your thumb can naturally point up to the z direction

4. i, j, k x y z

5. Vector equation of lines (in 3D) Find a vector equation of the line parallel to the z-axis through the point (3, 4, -7) Find a vector equation of the line through the points ( 2,5,7 ) and (1,4, 9). Find a vector equation of the line through i - 5j + 2k parallel to i - 2k

6. Intersection of lines Likely in 2-D not likely in 3-D

7. Skew lines In 3D lines which do not meet can be parallel or not parallel. If they do not meet and they are not parallel they are said to be skew lines

8. Example: Find where the lines r=(j - k) + s(i + 2j + k) and r=(i + 7j - 4k) +t(i + 3k) intersect

9. Practice qs Misc Ex 5 pages 70-71 qs 1, 2, 3, 4, 5