Shortest Distance Between Two Lines
Chapter Name : Three Dimensional Geometry |
Sub Topic Code : 104_12_11_05_02 |
Topic Name : Shortest Distance Between Two Lines |
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Sub Topic Name : Distance Between Two Skew Lines |
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Introduction
• Skew lines never intersect, although they appear to be. • They don’t exist in same plane and are not parallel too.
Pre-Requisites:
Skew lines, direction cosines, direction ratios, coplanar vectors, parallel lines.
Activity:
The diagonals drawn on the top side and lateral side of a cube form skew lines. Try to draw and figure out.
Real Life Question:
How far apart will be your palms if you hold one of the hands perpendicular to your body keeping the other down?
Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| Coplanar | Anything that lies in same plane. |
| Parallel lines | Lines that are in same direction but never intersecting. |
| Skew lines | Lines that straight but not coplanar or parallel and never intersecting. |
Learning aids / Gadgets
| Gadgets | How it can be used |
|---|---|
| A cube | Analyse its sides. |
| Your room | Open the door of your room |
Real life uses :
Skew lines are widely used in the field of construction.
Places to visit :
Open the door of your room. The top edge of the door and the side edge of the wall form skew lines.
Practical examples around us
| Examples | Explainations |
|---|---|
| A tree on the bank of a river | The tree and the stream are almost straight in different directions. But they never intersect since they exist in different planes. |
What you learn in Theory:
Skew lines are non intersecting lines in space. The shortest distance between them is the length of a line segment perpendicular to both the lines.
What you learn in Practice:
In a cube the horizontal edge (AB) on the front face and the vertical edge (CD) on the rear face of the cube are skew lines. The shortest distance between them can be the edge (BC) perpendicular to both.