## Monday, 20 March 2017

### THREE DIMENSIONAL GEOMETRY

THREE DIMENSIONAL GEOMETRY

While studying Analytical Geometry in two dimensions, and the introduction to three dimensional geometry, we confined to the Cartesian methods only. We will now use vector algebra to three dimensional geometry the purpose of this approach to 3-dimensional geometry is that it makes the study simple and elegant *.
In this chapter, we shall study the direction cosines and direction ratios of a line joining two points and also discuss about the equations of lines and planes in space under different conditions, angel between two lines, two planes, a line and a plane, shortest distance between two skew lines and distance of a point from a plane.Most of the above results are obtained in vector from. Nevertheless, we shall also translate these results in the Cartesian from which, at times, presents a more clear geometric and analytic picture of the situation.

### Intersection of subring

How to prove the intersection of two subrings is a subring? Let S1 and S2  be two subrings of a ring R. Then S1∩S2 is not empty since ...