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Unformatted text preview: Lecture 3: Lines and Planes in Three Dimensions May 7, 2009 Lecture 3: Lines and Planes in Three Dimensions Objectives 1 Define a parametric equations for curves in two dimensions. Lecture 3: Lines and Planes in Three Dimensions Objectives 1 Define a parametric equations for curves in two dimensions. 2 Find the equations of a line in three dimensions. parametric equations symmetric equations Lecture 3: Lines and Planes in Three Dimensions Objectives 1 Define a parametric equations for curves in two dimensions. 2 Find the equations of a line in three dimensions. parametric equations symmetric equations 3 Find the equation of a plane in three dimensions. Using a single point and a normal vector Using three points Lecture 3: Lines and Planes in Three Dimensions Objectives 1 Define a parametric equations for curves in two dimensions. 2 Find the equations of a line in three dimensions. parametric equations symmetric equations 3 Find the equation of a plane in three dimensions. Using a single point and a normal vector Using three points 4 Find the intersections of objects in three dimensions Lines with other lines Lines with planes Planes with other planes Lecture 3: Lines and Planes in Three Dimensions Objectives 1 Define a parametric equations for curves in two dimensions. 2 Find the equations of a line in three dimensions. parametric equations symmetric equations 3 Find the equation of a plane in three dimensions. Using a single point and a normal vector Using three points 4 Find the intersections of objects in three dimensions Lines with other lines Lines with planes Planes with other planes 5 Find the distance between objects in three dimensions A point and a plane Lines with other lines Planes with other planes Lecture 3: Lines and Planes in Three Dimensions Parametric equations. Instead of specifying a curve as y = y ( x ), we specify both coordinates as function of some parameter t . Lecture 3: Lines and Planes in Three Dimensions Parametric equations. Instead of specifying a curve as y = y ( x ), we specify both coordinates as function of some parameter t . There are two equations specifiying the curve, x = x ( t ) and y = y ( t ). Lecture 3: Lines and Planes in Three Dimensions Parametric equations. Instead of specifying a curve as y = y ( x ), we specify both coordinates as function of some parameter t . There are two equations specifiying the curve, x = x ( t ) and y = y ( t ). Imagine that a particle is traveling along the curve and that the parameter t represents time. Then at time t , the particle is at location ( x ( t ) , y ( t ))....
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 Spring '03
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 Equations, Multivariable Calculus, Parametric Equations

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