Three dimensional geometry, Mathematics

Three Dimensional geometry

Intorduction

In earlier classes we studied about the coordinates in two planes that is the XY plane. Here we are going to study in detail about the coordinates in three planes that is X, Y and the Z planes. First let us study about the direction cosines and direction ratios of lines.

1.     If the line makes angles α β γ with the positive directions of x- axis, y-axis and z-axis respectively then cos α , cos β , cosγ arecalled its direction cosines and are usually denoted as l,m,n.

2.     Direction cosines of x axis are 1,0,0

3.     Direction cosines of y-axis are 0,1,0

4.     Direction cosines of z-axis are 0,0,1.

Direction Ratios of a line.

1.     3 numbers a,b,c are called direction ratios of a line if l/a = m/b = n/c, where l,m,n are the direction cosines of the line.

2.     If l,m,n are the direction ratios of a line then l² + m² + n² = 1.

3.     If a line makes  α β γ  with the positive direction of x,y,z axes respectively then cos²α + cos²β + cos² γ = 1 and

4.     Sin²α+sin²β + sin²  γ  = 2.

 

6.     Direction ratios of the line joining A(x1,y1,z1) and B(x2,y2,z2) are x1-x2,

y1-y2, z1-z2 or vice versa.

Direction cosines of the line joining A(x1,y1,z1) and B(x2,y2,z2) are

x1-x2/AB, y1-y2/AB , z1-z2/AB

Posted Date: 7/23/2012 4:51:10 AM | Location : United States







Related Discussions:- Three dimensional geometry, Assignment Help, Ask Question on Three dimensional geometry, Get Answer, Expert's Help, Three dimensional geometry Discussions

Write discussion on Three dimensional geometry
Your posts are moderated
Related Questions
Five more than the quotient of a number and 2 is at least that number. What is the greatest value of the number? Let x = the number. Notice that quotient is a key word for div

volume=(1/3)(pi)(radius of base)2(height) curved surface area=(pi)(r)(l), r is radius of base and l is length of straight line connecting apex of cone with point on edge of base

theory behind the greatest term in the binomial expansion


One Tailed Test It is a test where the alternative hypothesis (H 1 :) is only concerned along with one of the tails of the distribution for illustration, to test a business co

the automatic hopper loader is set to put 36 tons of coal in each car. the actual weights of coal loaded into each car arw normally distributed with a mean of 36 tons and a standar

i need a step by step guide to answering simultaneous equation for gcses

The first section of a newspaper has 16 pages. Advertisements take up (3)3/8 of the pages. How many pages are not advertisements? Subtract the number of pages of advertisements

Question 1: (a) Show that, for all sets A, B and C, (i) (A ∩ B) c = A c ∩B c . (ii) A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C). (iii) A - (B ∪ C) = (A - B) ∩ (A - C).

The ratio between the length and breadth of a rectangular field is 11:7. The cost of fencing it is Rs. 75,000. Find the dimensions of the field