math 241 study guide - MATH 241 STUDY GUIDE: VC.01 Vectors:...

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MATH 241 STUDY GUIDE: VC.01 – Vectors: Adding and Subtracting Vectors ( basic ) Scalars in front of vectors Dot Product (multiply then add together) -Solve for variables within dot product -XdotY = IIxII*IIyII cos(b) -Dot > 0 then 0<=b<pi/2 -Dot<0 then pi/2<b<=pie Parametric and Parametrization (point) + DIRECTION (unit) Vector x variable Parallel – translate point Perpendicular – Direction Vector flip to make {y,-x} (3-D, z is 0) X push Y and Y push X -XpushY= (X*Y/Y*Y)Y Times by a unit vector which is divided by magnitude IIyII or IIxII VC.02 – Perpendiculary: Dot = # , Cross = Vector Cross Product Matrixes Line 1: i, j, k Line 2: First Vector Line3: Second Vector Write the same next to but just i and j DETERMINATES – UpDown Pos, Down Up Neg Planes a(x-_)+b(y-_)+c(z-_) = # {a,b,c} is normal vector Point on plane = solve for z or _ as a number equal to zero Parallel to plane is perpendicular to normal vector
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This note was uploaded on 01/27/2012 for the course CHEM 121 taught by Professor 1212 during the Spring '11 term at University of Illinois at Urbana–Champaign.

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math 241 study guide - MATH 241 STUDY GUIDE: VC.01 Vectors:...

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