Why Use Vectors? Learn About Vector Basics

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Discussion Overview

The discussion revolves around the concept of vectors, their definition, and their applications in physics. Participants explore the nature of vectors, how they represent direction and magnitude, and the importance of understanding them in the context of physics education.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants express confusion about the definition of vectors and their purpose in physics.
  • One participant explains that vectors indicate both direction and magnitude, using velocity as an example.
  • Another participant discusses how direction can be specified explicitly or through components, providing a mathematical breakdown of a velocity vector.
  • Some participants use analogies, such as comparing vectors to arrows or blades of grass, to illustrate the concept of direction and magnitude.
  • There is a debate about whether blades of grass can be considered to have direction, with some asserting they are only vertical while others argue they can bend in response to wind.
  • One participant suggests that the teacher may have assumed prior knowledge of vectors, leading to confusion among students.
  • Another participant emphasizes the utility of vectors in simplifying physics problems and enhancing understanding compared to historical methods of reasoning.
  • Participants discuss vector components and vector addition, with one providing a visual representation of how to add vectors graphically.
  • There is a question about the involvement of vectors when a force is exerted on a body, with a response affirming that forces are indeed vectors due to their strength and direction.

Areas of Agreement / Disagreement

Participants generally agree on the importance of vectors in physics and their defining characteristics. However, there remains disagreement and confusion regarding the definition of vectors, their representation, and the analogy of blades of grass, indicating that the discussion is not fully resolved.

Contextual Notes

Some participants express uncertainty about the teacher's explanation of vectors, suggesting a lack of clarity in the initial lecture. Additionally, there are unresolved questions regarding the nature of direction in various contexts, such as the orientation of grass blades.

Xidike
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Why We Use Vectors ?

I am new to this forum... nd Also new to physics... yesterday our teacher gives lecture about Vectors... but I can't understand any thing... doesn't know why ?
I want to ask that what are vectors and... Why we use vectors ?
 
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Xidike said:
I am new to this forum... nd Also new to physics... yesterday our teacher gives lecture about Vectors... but I can't understand any thing... doesn't know why ?
I want to ask that what are vectors and... Why we use vectors ?

Vectors are used to indicate the specific direction and the magnitude of the arrow or certain factor. For instance, velocity is a vector since it has direction and magnitude.
 


How they indicate the direction ??
 


Sometimes you state the direction explicitly: "the velocity is 25 m/s at 30° north of east".

Often you specify the vector using components, in which case the direction is implicit. The velocity given above would have vx = 21.65 m/s and vy = 12.50 m/s. This gives a magnitude of ##\sqrt{21.65^2 + 12.50^2} = 25## and a direction of ##\tan^{-1} (12.50/21.65) = 30°##.

(this assumes the x-axis is east/west and the y-axis is north/south).
 


Think of vectors as arrows on your axes (or in space), the value of the vector is represented by the difference between the head and the tail of the arrow.
 


Imagine you are in a big grassy field. All over the ground and everywhere you look there are blades of grass of every variety. Even though they are different, they all have a length and a direction.

Say you wanted to compare and record the blades of grass; one of the things which you would do is measure is their lengths and directions. This is a vector, and there are different ways which you could do this. You could get a ruler and measure their lengths and then use a compass to measure their directions, or you could set up a grid of reference directions across the whole field and measure how far the blades go in each direction, or even invent your own.

The way you measure the length and direction is called a coordinate system, and the way that you convert the measurements from one system into another is called a coordinate transformation.
 


Jasso said:
Imagine you are in a big grassy field. All over the ground and everywhere you look there are blades of grass of every variety. Even though they are different, they all have a length and a direction.

Say you wanted to compare and record the blades of grass; one of the things which you would do is measure is their lengths and directions. This is a vector, and there are different ways which you could do this. You could get a ruler and measure their lengths and then use a compass to measure their directions, or you could set up a grid of reference directions across the whole field and measure how far the blades go in each direction, or even invent your own.

The way you measure the length and direction is called a coordinate system, and the way that you convert the measurements from one system into another is called a coordinate transformation.

Here, what do you mean by the direction of blades ? :((:((:((
Aren't they only in vertical direction ?
 


"Aren't they only in vertical direction"
Really?
Go to the nearest field and have a look..
 


arildno said:
"Aren't they only in vertical direction"
Really?
Go to the nearest field and have a look..

But I've seen them only in vertical direction///\\\
 
  • #10


Xidike said:
But I've seen them only in vertical direction///\\\
What about the one you just stepped on?
Is that in a vertical direction??

Furthermore:
If there is wind, will the blades stand vertically?
 
  • #11


You said, in your first post, "yesterday our teacher gives lecture about Vectors". Now you appear to be saying that your teacher did NOT define "vectors" or give any real examples of vectors. That seems very strange. It may be that your teacher was assuming that you already knew what vectors are and was using a special case in a particular problem. You should talk to your teacher about that.

(And you confused things by titleing this "Why we use vectors" rather than, say, "What are vectors".)
 
  • #12


if there is a wind then, blades will only wave... but they will not walk or move from their position...
 
  • #13


I have never seen a field where the all of the grass sticks out of the ground completely vertically. Even if they aren't laying flat, they are always bent over in one direction or another. For example:

http://jeinc.publishpath.com/Websites/jeinc/Images/seed/Forage%20Grasses/bisonbuffforage.jpg

But, even if you did find a grassy field where they all stuck up vertically, that is still a vector, it has magnitude (the length of the grass) and direction (vertical).
 
  • #14


Others have answered "What are vectors". So "Why we use vectors?"

The answer is simple: Because once you understand them they make things easier. A whole lot easier. This simplicity opens up new ways of thinking.

You're taking physics, so certainly you've heard of Isaac Newton. If you read his principal work (which is *not* something I suggest you do), you will find it incredibly hard to read and understand. He doesn't use vectors. How could he? They were invented a couple of hundred years after his death. He doesn't use calculus, which was around at his time. He was one of the inventors of calculus. He barely uses algebra! The predominant mode of mathematical thinking in Newton's time was geometric reasoning.

Physics is a whole lot easier with algebra, vectors, and calculus than without. The mathematics might be a bit harder, but the physics is easier. You didn't mention whether you are taking algebra-based or calculus-based physics. Algebra-based physics is hard. It's one disparate fact after another that needs to be memorized. Add calculus and those disparate facts become variations on a theme.

It's much the same with vectors. They make things a lot easier and clearer -- once you learn them.
 
  • #15


I still can't clearly understand the concept of vector... and what is meant by the component of vector and vector addition ? :(:((:(((:((((:(((((
 
  • #16


I still can't clearly understand the concept of vector
It is an arrow
and what is meant by the component of vector
Here is a vector: (2,3), if we're using an x,y coordinate system then the x component of the vector is 2. The y component of the vector is 3.
y
|
|. / vector
| /
|/
+------------> x

and vector addition ?
If you add two vectors then you add the components, e.g. (2,3) + (1,2) is (3, 5)
Visually, imagine placing the second arrow's tail at the head of the first arrow.
 
Last edited:
  • #17


If we exert a force on a body... then, are there any vectors involving in it ?
 
Last edited:
  • #18


Xidike said:
If we exert a force on a body... then, are there any vectors involving in it ?
Yes.
A force has two basic features:
A strength, and a direction.
I can pull your nose downwards, sidewards or upwards, with different strength involved in all cases.
 

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