Shortest Distance Between Two Lines
Chapter Name : Three Dimensional Geometry |
Sub Topic Code : 104_12_11_05_01 |
Topic Name : Shortest Distance Between Two Lines |
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Sub Topic Name : Shortest Distance Between Two Lines |
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Introduction
• A 3d space is combination of 3 planes which are perpendicular to one another. • Lines drawn in a 3d space may be parallel, skew or intersecting. • The distance between two lines differs depending on the type. • The shortest distance is zero in case of intersecting lines.
Pre-Requisites:
Vector, 3d space, direction cosine, direction ratio, skew lines, parallel lines
Activity:
The shortest distance between the two edges of a ruler can be determined as the width of the ruler. The shortest distance between the skew lines of cube is the line segment perpendicular to both the diagonals.
Real Life Question:
The railroad has two parallel tracks, but do they appear to intersect at the end?
Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| Space | Combination of different plane. |
| Parallel lines | Lines which exist in same plane or different plane and never intersect. |
| Skew lines | Lines which exists different planes and never intersect. |
Learning aids / Gadgets
| Gadgets | How it can be used |
|---|---|
| Ruler | The two edges of ruler are parallel. |
| A cube | The diagonals of two adjacent faces are skew. |
Real life uses :
The shortest distance between two lines are calculated while constructing roads, rail tracks for smooth travelling and used in building constructions too.
Places to visit :
Check your class room to find parallel lines. E.g., edges of table, the grill rods of a window. Some skew lines can be found in your room. The top edge of a opened door and a line drawn on your wall.
Practical examples around us
| Examples | Explainations |
|---|---|
| The road you are travelling | The road lines are always parallel and the distance between them is the length of perpendicular line connecting them. |
| The cross bridge over railway track | They both form skew lines and the shortest distance is the length of the line perpendicular to both. |
What you learn in Theory:
However we draw two lines in space, we can always find a shortest distance between them by drawing line segment perpendicular to both the end lines.
What you learn in Practice:
The shortest distance between the rail tracks is the width of the rail road.