Equation Of A Line Space
Chapter Name : Three Dimensional Geometry |
Sub Topic Code : 104_12_11_03_01 |
Topic Name : Equation Of A Line Space |
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Sub Topic Name : Equation Of A Line Through A Given Point And Parallel To A Given Vector |
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Introduction
Equation of vector and parametric equations model physical situations related to motion.
Pre-Requisites:
Knowledge of vectors, direction ratios, direction cosines.
Activity:
You can observe parametric equations describe the same line as y=-3x+6.
Real Life Question:
Suppose you travel on highway number 24(Delhi-Agra) with a constant velocity v (75,-60)km/hr. How far south of Delhi are you when you are at a position 100km east of Delhi?
Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| Three dimensional geometry | An object that has height, width and length. |
| Vector equation | An equation involving vectors. Using vector equation we can find position vector of any given point on line. |
| Parametric equation | An equation involving parameters. |
Learning aids / Gadgets
| Gadgets | How it can be used |
|---|---|
| Graph paper | Consider parametric equation y = -3x+6. In the equation x is the independent variable and y is dependent variable. In parametric Equations t is independent and x ,y are dependent. If we set independent variables x, t equal we have two equations as x =t, and y =-3t+6. Make a table of values of t and find x, y. Plot these values on graph. What do you observe for parametric equation of t and the equation of y. |
Real life uses :
Vector equations and parametric equations model physical situations like air race where t represents time in hours can be used in navigation to know path of target.
Practical examples around us
| Examples | Explainations |
|---|---|
| Air race | With vector equations and parametric equations we can Model physical situations like finding distance planes have travelled in air race. |
What you learn in Theory:
In parametric equations t is independent variable and x and y variables are dependent. Parametric equation is of the form x = x?+ta.
What you learn in Practice:
Physical situations relating to distance, time and speed can be modeled by parametric And vector equations.