Lines and Planes Ch13.5.

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Presentation transcript:

Lines and Planes Ch13.5

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:

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

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!

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