Multiplication Of A Vector By A Scalar
Chapter Name : Vector Algebra |
Sub Topic Code : 104_12_10_05_01 |
Topic Name : Multiplication Of A Vector By A Scalar |
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Sub Topic Name : Multiplication Of A Vector By A Scalar |
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Introduction
In mathematics, scalar multiplication is one of the basic operations defining a vector space in linear algebra. In an intuitive geometrical context, scalar multiplication of a real Euclidean vector by a positive real number multiplies the magnitude of the vector without changing its direction. The term "scalar" itself derives from this usage: a scalar is that which scales vectors. Scalar multiplication is the multiplication of a vector by a scalar (where the product is a vector), and must be distinguished from inner product of two vectors (where the product is a scalar).
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.
Real Life Question:
How do you stretch or shrink a vector?
Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| Scalar Quantity | A scalar is a quantity which can be described by a single number, unlike vectors, tensors, etc. which are described by several numbers which describe magnitude and direction. |
| 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. |
Learning aids / Gadgets
| Gadgets | How it can be used |
|---|
Real life uses :
An airplane landing in a crosswind is a real-world example of vector addition. When a strong wind blows across a runway, the pilot must aim the plane into the wind so that a component of the plane's velocity will cancel the crosswind. The key is to get the resultant velocity vector to point directly along the runway.
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 scalar multiplication of a vector.
What you learn in Practice:
We apply concept of scalar multiplication to shrink and stretch a vector.