Direction Cosines And Direction Ratios Of A Line
Chapter Name : Three Dimensional Geometry |
Sub Topic Code : 104_12_11_02_01 |
Topic Name : Direction Cosines And Direction Ratios Of A Line |
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Sub Topic Name : Direction Cosines And Direction Ratios Of A Line |
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Introduction
• Direction ratios provide a convenient way of specifying direction of a line in three dimensional space. • Direction cosines are cosines of angle between line and co-ordinate axes.
Pre-Requisites:
Knowledge of vectors.
Activity:
This task will help in finding direction cosines of a line if direction ratios are given.
Real Life Question:
A chimney is built in right corner of a building and is protected from high winds by three wires attached to corners of building. If the building inspector wants to find angle between the directions of the wires which angle he will find out?
Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| Three dimensional geometry | An object that has height, width and length. |
| Direction ratios | Direction ratios are also called as direction numbers. |
Learning aids / Gadgets
| Gadgets | How it can be used |
|---|---|
| Graph paper | Draw a three co-ordinate plane on graph paper and take direction ratios as 30 degree, 45 degree and 90 degree. Find direction cosines. |
Real life uses :
The concept of direction ratios and direction cosines is useful in ray tracing.
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:
Direction ratios and direction cosines are important in learning 3D geometry.