lecture02

lecture02 - MATH 100 Lecture 2 Parametric Equation Lines...

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2006 Fall MATH 100 Lecture 2 1 MATH 100 Lecture 2 Parametric Equation Lines () 000 00 0 Theorem 1 (a) In 2-space, the line passes through , and parallel to , has the parametric equations , (b) In 3-space, the line passes through , , Pxy va ba i b j xx a t yy b t Pxyz == + =+ GG G 0 and parallel to , , has the parametric equations , , v abc a i b j ck a t bt z z ct + + = += + = + G G
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2006 Fall MATH 100 Lecture 2 2 ( ) 0 00 0 Proof: For a point , , on the line, , i.e. , , , , , , Equating the components we can end up the conclusions Px y z P P t v x x y y z z t abc tatbtc == −−− = = G MATH 100 Lecture 2 Parametric Equation Lines
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2006 Fall MATH 100 Lecture 2 3 () ( ) k j i v P v P G G G G G 7 5 4 , 3 , 2 , 1 (b) 5 , 1 , 2 , 4 (a) followings the of equations parametric the Find : Ex 0 0 + = = = = t z t y t x t y t x 7 3 , 5 2 , 4 1 (b) 5 2 , 4 (a) : Sol = + = + = + = = MATH 100 Lecture 2 Parametric Equation Lines
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2006 Fall MATH 100 Lecture 2 4 () ( ) 7 0 5 and 1 4 2 joining that line for the equations parametric the Find : Ex 2 1 , , P , , P 12 1 01 Sol: 3, 4,8 2 3 , 4 4 , 1 8 and are corespond to 0 and 1 vP P rP t v xt y t z t PP t t == =+ =− = + G GG MATH 100 Lecture 2 Parametric Equation Lines
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This note was uploaded on 09/17/2011 for the course MATH 100 taught by Professor Qt during the Fall '09 term at HKUST.

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lecture02 - MATH 100 Lecture 2 Parametric Equation Lines...

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