Equation Of A Line Space
Chapter Name : Three Dimensional Geometry |
Sub Topic Code : 104_12_11_03_02 |
Topic Name : Equation Of A Line Space |
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Sub Topic Name : Equation Of A Line Passing Through Two Given Points |
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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 direction vector is coefficients of t terms.
Real Life Question:
Suppose in a car racing competition, the distance of runway path is 500 miles. The speed of two cars is 80 and 90m/hr. How much time is required for slower car to overtake the faster car?
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 | If x =3-4t, y= 3t, z = -5+t. Find the direction vector and points of coordinates. |
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?+t(x?-x?).
What you learn in Practice:
Physical situations relating to distance, time and speed can be modeled by parametric And vector equations.