MATH 32A Lecture 6: Unpacking the equation
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In class wefoundtheequation of a plane basedonthegeometry howcan we readout the geometry put another way what do abc d measure in axtbyi. cz d. F x xoyyo2 7 0 x x yyo2 7 4 yz xoyozd so theequation is equivalent to it noyo207. F xyz f xoyo2o o or f x y z. Example then it is 4,0d rt lab c. 3 2y72 4 then n 3,2 7 ie we can read it as thecoefficients it is 21 2 4. Inthiscase d is f xoyo o for any xoyo2o ortheplane so whatdoes thismeasure geometrically. Considertheline through the origin parallel to it thisline is uniqueeventhough it is not ingeneral theline hastheform ptt tri this hitsthe plane at some to recto pointsto a point ortheplane so tohillin torn d. Thisexplains what d does to 41117112 so ryto n e 3.
