Lecture 10-5 - 1 2 4 Defn Equation of a plane Given a point...

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10.5 Lines and Planes Introduction to 3-space ( R 3 ) Example 1 Graph x = 2 In R 2 . In R 3 . 1
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Lines What determines a line? In R 2 : In R 3 : The Equation of a Line In R 2 : In R 3 : Defn. Parametric Equations of a Line Given a point P ( x 0 , y 0 , z 0 ) on the line L and a vector ~v = < a, b, c > parallel to the line L , the parametric equations of the line L are 2
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Defn. Vector Equation of a Line Given a point P ( x 0 , y 0 , z 0 ) on the line L and a vector ~v = < a, b, c > parallel to the line L , the vector equation of the line L is Example 1 Find the equation of (or ”parameterize”) the line that passes through P (4 , 0 , 6) and Q (1 , 1 , - 1). Example 2 Graph the line x = 2 + t y = - 3 z = 3 t 3
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Planes Equation of a plane Graph by finding x , y , z intercepts. Example 1 Graph 2 x + y - z = 4. Example 2 Graph 2 x + y = 4. What determines a plane?
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Unformatted text preview: 1. 2. 4 Defn. Equation of a plane Given a point P ( x , y , z ) on the plane and a vector ~n = < a, b, c > normal to the plane, the equation of the plane is OR Example 1 Find the equation of the plane through P (4 , , 6) normal to ~n = <-1 , 7 , 3 > . Example 2 Find the equation of the plane through the origin which contains the line x = 2 + t y =-1 z =-2 t. 5 Example 3 Find the equation of the plane through the points P,Q,R. Example 4 Find the equation of the line formed from the intersection of 3 x-6 y-2 z = 3 and 2 x + y-2 z = 2. 6...
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This note was uploaded on 03/03/2010 for the course MATH 2224 taught by Professor Mecothren during the Spring '03 term at Virginia Tech.

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Lecture 10-5 - 1 2 4 Defn Equation of a plane Given a point...

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