Ch12s5 - 12.5 Equations of Lines and Planes A line L is determined by a point P0 x0 y0 z0 on L and the direction of L The direction of a line is

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12.5 Equations of Lines and Planes A line L is determined by a point on L and the direction of L. The direction of a line is described by a vector. ( 0000 ,, Pxyz ) - vector parallel to L point on L - posi epresentation vectors) - riangle Law for vector addition gives a r lar such that v . v r v (, ,) xyz - an arbitrary P rr tion vectors of P 0 and P (r 0 , r vector with representation P uuur a 0 P T 0 =+ a r and v r are parallel and there is a sca t at = 0 t rr r is the vector equation of L. ach value of the parameter gives the position vector of a point on L. corresponds to points on L on one side of P 0 . of P 0 . : vector that gives the direction of L E t r r 0 > corresponds to points on L on the other side t 0 t < v r abc = is the direction of L in co r v tv ta tb tc = r , , , r x y z = mponent form from which we can get . 00 0 rx y z = 0 The vector equation of the line r comes 0 rrt v be 000 if the corresponding components are equal. P(x,y,z) r x y z L v P 0 (x 0 ,y 0 ,z 0 ) r 0 t=0 t>0 t<0 r 0 a , , x y z x ta y tb z tc + + Two vectors are equal if and only
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The parametric equations of the line L
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This note was uploaded on 01/20/2012 for the course MATH 2057 taught by Professor Estrada during the Fall '08 term at LSU.

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Ch12s5 - 12.5 Equations of Lines and Planes A line L is determined by a point P0 x0 y0 z0 on L and the direction of L The direction of a line is

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