mthsc206-fall-2010-notes-13.1 - 13 13.1 Vectors and the Geometry of Space Three-Dimensional Coordinate System graphing in 1-dimension and 2-dimensions

# mthsc206-fall-2010-notes-13.1 - 13 13.1 Vectors and the...

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13Vectors and the Geometry of Space13.1Three-Dimensional Coordinate SystemTools:graphing in 1-dimension and 2-dimensionsdistance formula on the real number linedistance formula in the planePythagorean Theoremcompleting the squareRecall the coordinate systems for 1-dimensional (real number line) and 2-dimensional (the plane) spaces.We want to generalize to 3-dimensions and beyond.What does the coordinate system look like for a 3-dimensional space? Beyond?What is the right-hand rule? Where does this put the positivez-axis? Where would a left-hand ruleplace the positivez-axis?Describe the solutions to the equationsx= 0,y= 0,z= 0,x=a,y=b,z=c.What would the solutions to the equationy=xlook like?y= sinx?x2+y2= 4?Problem 13.1.1LetP0(x0, y0, z0)andP1(x1, y1, z1)be two points in 3-space. Determine the formula for the distance betweenP0andP1.Here are your only tools:
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