1. Lines and Planes
Ch13.5

2. How to build a line… Start with a point in R3
Use this point to define a starting vector r0
Pick a direction and a vector v that points in that direction
Use a parameter ‘t’ to define:

3. Parametric Equation of a Line in R3
Use
Let r = <x,y,z>, ro = <5,1,3>, v = <1,1,-2>, then:
This can be written as a set of parametric equations: ?
How can you eliminate ‘t’ from this to get an equation in x,y,and z

4. From lines to planes… How many planes can contain a line?
How can we define a unique plane?
A plane is defined by its normal vector!

5. Linear form…
Example: find the equation of the plane that contains the points A(2,-1,4), B(1,2,6), and C(-2,1,-4)
examples 13.5: 5, 12,19, 68