Analytical Solid Geometry
chap-03 B.V.Ramana August 30, 2006 10:22 Chapter 3 Analytical Solid Geometry 3.1 INTRODUCTION Rectangular Cartesian Coordinates In 1637, Rene Descartes* represented geometrical The position (location) of a point in space can be figures (configurations) by equations and vice versa. determined in terms of its perpendicular distances Analytical Geometry involves algebraic or analytic (known as rectangular cartesian coordinates or sim- methods in geometry. Analytical geometry in three ply rectangular coordinates) from three mutually dimensions also known as Analytical solid** geom- perpendicular planes (known as coordinate planes). etry or solid analytical geometry, studies geometrical The lines of intersection of these three coordinate objects in space involving three dimensions, which planes are known as coordinate axes and their point is an extension of coordinate geometry in plane (two of intersection the origin. dimensions). The three axes called x-axis, y-axis and z-axis are marked positive on one side of the origin. The pos- itive sides of axes OX, OY, OZ form a right handed system. The coordinate planes divide entire space into eight parts called octants. Thus a point P with coordinates x,y,z is denoted as P (x,y,z). Here x,y,z are respectively the perpendicular distances of P from the YZ, ZX and XY planes. Note that a line perpendicular to a plane is perpendicular to every line in the plane. Distance between two points P1(x1,y1,z1) and − 2+ − 2+ − 2 P2(x2,y2,z2)is (x2 x1) (y2 y1) (z2 z1) . 2 + 2 + 2 Distance from origin O(0, 0, 0) is x2 y2 z2.
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