handout 12-2 and 12-5

handout 12-2 and 12-5 - Math 200, Spring 2010 Handout 3...

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Math 200, Spring 2010 Handout 3 Section 12-2 Parametric Equations of a Line Section 12-5 Planes in Three-Space Vector Equation of Line L in Three Space (Point-Direction Form) The line L through point 0 0 0 0 ( , , ) P x y z in the direction of , , a b c = v , where ( ) , , P x y z is an arbitrary point on L and 0 r and r are position vectors of 0 P and P , is described by Vector Parametrization: 0 0, 0, 0, , , t x y z t a b c = + = + r r v The vector v is called a direction vector for line L . A direction vector for a line is a substitute for the slope (which only makes sense in the plane). However, the direction vector is not unique - any nonzero scalar multiple of v is also a direction vector for line L . 1. Find a vector equation for the line through the point (3, 1,4) and parallel to the vector 2 7 + + i j k . Parametric and Symmetric Equations of Line L in Three Space The line L through point 0 0 0 0 ( , , ) P x y z in the direction of , , a b c = v is described by Parametric equations: 0 0 0 , , x x at y y bt z z ct = + = + = + Symmetric equations: 0 0 0 x x y y z z a b c = = The numbers a , b , and c are called direction numbers of L . Any three numbers proportional to a , b , and c could also be used as a set of direction numbers for L . 2.
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handout 12-2 and 12-5 - Math 200, Spring 2010 Handout 3...

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