Direction Cosines And Direction Ratios Of A Line
Chapter Name : Three Dimensional Geometry |
Sub Topic Code : 104_12_11_02_03 |
Topic Name : Direction Cosines And Direction Ratios Of A Line |
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Sub Topic Name : Direction Cosines Of A Line Passing Through Two Points |
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Introduction
• Direction cosines are cosines of angle between line and co-ordinate axes. • Direction cosines of a line passing through two points is given by Cosine angle = length of the vectors/length of position vector.
Pre-Requisites:
Knowledge of vectors, direction ratios, direction cosines.
Activity:
You can find direction cosine by applying equation of direction cosine of line passing through two points.
Real Life Question:
Suppose two persons are moving a stretcher and first person is moving stretcher at 110 newton at 58 degree horizontal and other person is moving stretcher at 48 degree horizontal. What is magnitude of force exerted on stretcher?
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 |
|---|---|
| Wooden stick, string | Put wooden stick vertical and tie two strings to it. Imagine a tower this is supported by two cable wires. Measure distance between two strings and length of stick. Can you find direction cosine. |
Real life uses :
Direction cosines are useful in calculating geographic relationship between surface objects, magnitude, angles.
Practical examples around us
| Examples | Explainations |
|---|---|
| Length of tower. | If a mobile tower is constructed on a building and it is supported by two cable wires such that it makes an angle 90? and the ground distance between the two cables is 40m. Then what is the length of the mobile tower? We apply equation of direction cosine of line passing through two points to get the length of tower. |
What you learn in Theory:
Direction cosines = length of vectors/length of position vector.
What you learn in Practice:
With the help of direction cosines calculations for magnitude, angles becomes easy as compared to sine, cosine and tangent functions.