mthsc206-fall-2010-notes-13.5

mthsc206-fall-2010-notes-13.5 - 13.5 Equations of Lines and...

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13.5 Equations of Lines and Planes Lines in 3-space Question: What determines a line in 2-space? 3-space? Defnition 13.5.1 The line through the point P 0 ( x 0 ,y 0 ,z 0 ) parallel to the vector v = <v 1 ,v 2 ,v 3 > is given by Example 13.5.1 Find parametric equations for the line through the points P (2 , 4 , - 1) and Q (5 , 0 , 7) . Find parametric equations for the line segment beginning at P and ending at Q . Problem 13.5.1 Given parametric equations for the points on a curve, how do you eliminate the param- eter? For example: if x = sin t, y = cos t, eliminate the parameter to ±nd a cartesian equation of the curve. Defnition 13.5.2 The symmetric equations for the line with given parametric equations x = x 0 + v 1 t, y = y 0 + v 2 t, z = z 0 + v 3 t are x - x 0 v 1 = y - y 0 v 2 = z - z 0 v 3 . Problem 13.5.2 How do you determine whether two lines are parallel? Defnition 13.5.3 To lines are skew if they are not parallel and do not intersect. Problem 13.5.3
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This note was uploaded on 10/11/2010 for the course MTHSC 206 taught by Professor Chung during the Spring '07 term at Clemson.

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mthsc206-fall-2010-notes-13.5 - 13.5 Equations of Lines and...

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