Some Basic Concepts
Chapter Name : Vector Algebra |
Sub Topic Code : 104_12_10_02_01 |
Topic Name : Some Basic Concepts |
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Sub Topic Name : Types of vectors |
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Introduction
A vector is a geometric object that has magnitude and direction and can be added to other vectors according to vector algebra. ) If there is a point P with coordinates (x, y, z) with respect to the origin O (0, 0, 0), then the vector OP is called the position vector. The angles ?,?, ? made by the vector r with the positive directions of x, y and z-axes respectively are called direction angles and the cosine values of these angles, i.e., cos?, cos? and cos ? are called direction cosines of the vector r.
Pre-Requisites:
• Coordinate Axes • Geometry Basics • Knowledge of displacement, force, pressure, acceleration etc.
Activity:
Observe the direction and force you apply when you open a door/ push a chair/open a can of Jam. Also, observe the acceleration of your car/bus while driving to school.
Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| Vector Quantity | A vector is a geometric object that has magnitude and direction and can be added to other vectors according to vector algebra. |
| Magnitude | Magnitude is a term for the size or length of a vector. |
| Direction | It is the Relative direction, for instance left, right, forward, backwards, up, and down. |
| Position Vector | If there is a point P with coordinates (x, y, z) with respect to the origin O (0, 0, 0), then the vector OP is called the position vector. |
| Direction Cosines | The angles ?,?, ? made by the vector r with the positive directions of x, y and z-axes respectively are called direction angles and the cosine values of these angles, i.e., cos?, cos? and cos ? are called direction cosines of the vector r. |
Learning aids / Gadgets
| Gadgets | How it can be used |
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Real life uses :
Vector algebra helps us solve complex trigonometric and geometric problems. It is used extensively in computational mechanics. The vector Algebra biquaternions and hyperbolic quaternions enabled the revolution in physics called special relativity by providing mathematical models.
Practical examples around us
| Examples | Explainations |
|---|---|
| Breathing | Your diaphragm muscles exert a force that has a magnitude and direction. |
| Walking | You walk at a velocity of around 6 km/h in the direction of your park. |
What you learn in Theory:
We learn about vectors, position vectors, direction cosines and their applications.
What you learn in Practice:
We observe how and why the concept of vectors is applied in our daily lives.