Product Of Two Vectors
Chapter Name : Vector Algebra |
Sub Topic Code : 104_12_10_06_02 |
Topic Name : Product Of Two Vectors |
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Sub Topic Name : Projection Of A Vector On A Line |
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Introduction
Suppose a vector A?B? makes an angle ? with a given directed line l, in the anticlockwise direction. Then the projection of A?B? on l is a vector p? with magnitude | A?B?| cos?, and the direction of p? being the same (or opposite) to that of the line l, depending upon whether cos? is positive or negative. The vector p? is called the projection vector, and its magnitude |p?| is simply called the projection of the vector A?B? on the directed line l.
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 find if 3 points are collinear?
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. |
| Direction | It is the Relative direction, for instance left, right, forward, backwards, up, and down. |
| Projection Vector | The projection of A?B? on l is a vector p? with magnitude | A?B?| cos?, and the direction of p? being the same (or opposite) to that of the line l, depending upon whether cos? is positive or negative. The vector p? is called the projection vector, and its magnitude |p?| is simply called the projection of the vector A?B? on the directed line l. |
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 how to find the projection of a vector on a line.
What you learn in Practice:
We learn how to find if 3 points are collinear.