Direction Cosines And Direction Ratios Of A Line
Chapter Name : Three Dimensional Geometry |
Sub Topic Code : 104_12_11_02_02 |
Topic Name : Direction Cosines And Direction Ratios Of A Line |
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Sub Topic Name : Relation Between The Direction Cosines Of A Line |
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Introduction
• Direction cosines are cosines of angle between line and co-ordinate axes. • In this section we will find relation between direction cosines of a line.
Pre-Requisites:
Knowledge of vectors, direction ratios, direction cosines.
Activity:
You will observe only two direction cosines represented in numbers on earth’s map.
Real Life Question:
Which relationship of direction cosines is used in calculating geographic relationship between surface objects?
Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| Three dimensional geometry | An object that has height, width and length. |
| Direction cosines | Direction cosines are defined as the cosines of angles between line and coordinate axes. |
Learning aids / Gadgets
| Gadgets | How it can be used |
|---|---|
| Website(earth coordinates) | Direction cosines are used for describing earth’s co-ordinates. |
Real life uses :
Direction cosines are useful in calculating geographic relationship between surface objects, latitude longitude coordinate axes.
Practical examples around us
| Examples | Explainations |
|---|---|
| Reflected ray | Direction cosines are used to trace path of reflected light ray. Reflected light ray concept is used in optics, microscope and telescope. |
What you learn in Theory:
Direction cosines of a line are unique but direction ratios of line are infinite.
What you learn in Practice:
With the help of direction cosines calculations for spatial relationships becomes easy as compared to sine, cosine and tangent functions.