Prelim #1 Cheat Sheet

Prelim #1 Cheat Sheet - V e c to r O p e ra ti o n s: D o t...

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Unformatted text preview: V e c to r O p e ra ti o n s: D o t P ro d u c t: u v u v cos u 1 v1 u 2 v 2 u a n d v a re o rth o g o n a l v e c to rs if u v 0 p ro j v u u cos v v u v 2 v v u 3v3 S c a la r c o m p o n e n t u in d ire c tio n o f v T o e x p r e ss u a s a V e c to r P a ra le ll C ro ss P ro d u c t: u v u v sin A re a o f P a ra lle lo g ra m = u v i u v u1 v1 j u2 v2 k u3 v3 v w -1 u cos v u v u p ro j v u u p ro j v u to v p lu s a V e c to r o rth o g o n a l to v : n u v sin n u v sin V o lu m e o f P a ra lle le p ip e d = u A n g le B e tw e e n T w o V e c to rs: u u v u v v w cos a re a o f b a se h e ig h t = cos L in e s a n d P la n e s in S p a c e P a ra m e te riz in g E q u a tio n s o f a L in e th ro u g h P 0 ( x 0 , y 0 , z 0 ) p a ra lle l to v x x 0 tv1 , y y 0 tv1 , z z 0 tv 3 V e c to r fro m P o in t A to P o in t B : A B ( B x A x ) i ( B y A y ) j ( B z L in e fro m a P o in t a n d a V e c to r: P 0 ( x 0 , y 0 , z 0 ) , v Ai Bj C k L: D ista n c e fro m a P o in t S to a L in e T h ro u g h P P a ra lle l to v : L: x x0 At, y y0 Bt, z z0 C t , S ( x , y , z ) , P (x 0 , y 0 , z 0 ) , v Ai By Bj Cz Ck : D v1 i v2 j v3k : Az)k x x0 At, y y0 Bt, z PS v v z0 Ct Ai Bj Ck , d T h e p la n e th ro u g h P0 ( x 0 , y 0 , z 0 ) n o rm a l to n A( x x0 ) B(y y0 ) C (z z0 ) 0 Ax A v e c to r p a ra lle l to th e L in e o f In te rse c tio n o f T w o P la n e s: T a k e th e c ro ss p ro d u c t o f th e ir n o rm a ls n D ista n c e fro m a P o in t S to a P la n e : d PS n S is a p o in t o n th e p la n e (in te rc e p t) a n d n A i B j C k is n o rm a l to th e p la n e ...
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This note was uploaded on 06/01/2008 for the course MATH 1920 taught by Professor Pantano during the Spring '06 term at Cornell.

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