Why Use Vectors? Learn About Vector Basics

[Xidike]

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 ?

 

[NasuSama]

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.

 

[Xidike]

How they indicate the direction ??

 

[jtbell]

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 v_x = 21.65 m/s and v_y = 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).

 

[TGlad]

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.

 

[Jasso]

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.

 

[Xidike]

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 ?

 

[arildno]

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

 

[Xidike]

"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///\\\

 

[arildno]

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?

 

[HallsofIvy]

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".)

 

[Xidike]

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

 

[Jasso]

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).

 

[D H]

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.

 

[Xidike]

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

 

[TGlad]

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.

 

[Xidike]

If we exert a force on a body... then, are there any vectors involving in it ?

 

[arildno]

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.