Addition Of Vectors
Chapter Name : Vector Algebra |
Sub Topic Code : 104_12_10_04_01 |
Topic Name : Addition Of Vectors |
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Sub Topic Name : Addition Of Vectors |
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Introduction
If we have two vectors a and b then to add them, they are positioned so that the initial point of one coincides with the terminal point of the other.Then, the vector a + b , represented by the third side AC of the triangle ABC, gives us the sum of the vectors a and b. This is known as the triangle law of vector addition. If we have two vectors A and B represented by the two adjacent sides of a parallelogram in magnitude and direction (Fig 10.9), then their sum A+B is represented in magnitude and direction by the diagonal of the parallelogram through their common point. This is called Parallelogram Law of Addition.
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:
Amy travels from her home (A) to School (B) in the morning. After school she travels to the book store(C) to get some school books. What is the net displacement made by her from home to book store (AC)?
Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| Triangle Law of Vector Addition | If we have two vectors a and b then to add them, they are positioned so that the initial point of one coincides with the terminal point of the other.Then, the vector a + b , represented by the third side AC of the triangle ABC, gives us the sum of the vectors a and b. |
| Parallelogram Law of Vector Addition | If we have two vectors A and B represented by the two adjacent sides of a parallelogram in magnitude and direction (Fig 10.9), then their sum A+B is represented in magnitude and direction by the diagonal of the parallelogram through their common point. This is called Parallelogram Law of Addition. |
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 vector addition and its properties.
What you learn in Practice:
We observe how and why the concept of vectors is applied in our daily lives.