12.1 Three- dimensional Coordinate systems - Math 253 Calculus III 12.1 Three-Dimensional Coordinate Systems Written by Giriraj Bhattarai We

12.1 Three- dimensional Coordinate systems - Math 253...

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Math 253: Calculus III 12.1 Three-Dimensional Coordinate SystemsWritten by Giriraj BhattaraiWe represent a point in a plane by an ordered pair(a,b)of real numbers, whereais thex-coordinate andbis they-coordinate. We represent any point in space by an ordered triple(a,b,c)of real numbers.In order to represent points in space, we first choose a fixed pointO, called theorigin, and three directedlines throughOthat are perpendicular to each other , called thecoordinate axesand labeled thex-axis,y-axis, andz-axis as in figure below.OyzxThe three coordinate axes determine the threecoordinate planesillustrated in figure below. Thexy-plane is the plane that contains thex- axis andy-axis; theyz-plane is the plane that contains they- axisandz-axis; thexz-plane is the plane that contains thex- axis andz-axis. These three coordinate planesdivide space into eight parts; calledoctants. Thefirst octantis the octant determined by the positivesaxes.To locate a point(a,b,c)

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