Multiplication Of A Vector By A Scalar
Chapter Name : Vector Algebra |
Sub Topic Code : 104_12_10_05_03 |
Topic Name : Multiplication Of A Vector By A Scalar |
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Sub Topic Name : Section Formula |
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Introduction
If vector joins two points with P?1 having coordinates (x1, y1, z1) and point P?2 having coordinates (x2, y2, z2) then the line joining the two Vectors P?1 and P?2 is vector P1?P?2.
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:
If I am standing at point P?1 with coordinates (x1, y1, z1) and Suzy is standing at point P?2 (x2,y2,z2) then the line joining P1 and P2 describes which 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 is 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 |
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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 a vector joining two points.
What you learn in Practice:
We learn how to calculate a vector joining two points and its magnitude.