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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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1 1 2 2 3 3 2 D ot Product: cos and are orthogonal vectors if 0 cos Scalar com ponent in direction of cos T o V ecto e r O perati xp o r ns: v u v u v u v u v u v u v u v v u v proj u u v v v v u v u u v       1 2 3 1 2 3 ess as a V ector Paralell to plus a V ector orthogonal to : C ross Product: sin A rea of Parallelogram = sin sin V olum e of v v u v v u proj u u proj u u v u v n u v u v n u v i j k u v u u u v v v -1 0 0 0 0 Parallelepiped = cos area of base heig ht A ngle B etw een T w o V ecto Lines and rs: = cos Param eterizing E quation Planes in Space s of a Line through P ( , , ) p u v w u v w u v u v x y z   1 2 3 0 1 0 1 0 3 0 0 0 0 0 arallel to : , y , z V ector from Point A to Point B : ( ) ( ) ( ) Line from a Point and a V ector: P ( , , ) , L: v v i v j v k x x tv y tv z tv A B B x A x i B y A y j B z A z k x y z v A i B j C k x x A 
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