Three Dimensional Analytic Geometry, Assignments of Basic Electronics

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THREE DIMENSIONAL ANALYTIC GEOMETRY a The subject.of geometry is almost as old as the human civilization. The famous Greek mathematician, Euclid wrote thirteen books geometry during 330 to 275 B.C. With the passage of time many developments in this subject occurred and in the seventeenth century a French mathematician and philosopher Rene ‘Descarte(1596-1650 A.D) introduced the coordinate Geometry which proved to be a revolution in the field of Geometry. on the subject of Two-dimensional analytic geometry was discussed in article 0.8. In the article 0.12 vectors were discussed both in the two dimensional plane R? and three dimensional space R°. In this chapter Analytic Geometry ‘of three dimensions is presented. Whenever necessary vector approach has been adopted. ; 8.1 THE STRAIGHT LINE As the reader is familiar with the two dimensional analytic geometry and the three dimensional space R? , therefore we start with the concept of the distance between two points in R°. Direction ratios and direction cosines of a line, conditions of parallelism and perpendicularity of two lines, angle betweei , the coplanar and the skew lines and the shortest distance between them are also discussed in this section. 8.1.1 Distance Between Two Points Consider two points P; and P2 in the three-dimensional: space. Let the coordinates of P; and P2 be (x1 , ¥1 , 21) and (2, 2, 22) respectively. Construct a 516 Scanned with CamScanner