What is Vector, If you want to know simple vector meaning. Then first understand vector definition. Because it is different from other physical quantity. So its operation is called vectors math. Which is different from general math. And its representation is called vector images. Which allow vector rule addition. Hence learn here vector best concept.
Today our topic is very important for physics. What is Vector ? It is important because physics is teach through, two methods one is vector and other is calculus. vector method is easy to teach Physics. And learning is easy. so you can understand the importance of vector.
All important physical quantity in physics are vectors. without vector physics is poor. In previous post we have discussed some little about Vector. This is topic of mathematics but we study in physics. Because mathematics is tool of physics, just like Gun is arms of soldier. Hence mathematics is arms for physicist. So lets start.
Coordinate system: very first do you know. what is coordinate system ? Suppose you go to college or office every day. And on your birthday. You have invited your friend to join your birthday party. Then your friend ask you, how much distance is your home from college.
Hence how do you calculate distance of your home, from your college . Simple there are always two point to calculate distance between them. In this case your college and your home are two points. If you want to calculate distance from college to home. Then you can fixed the origin (not moving point ) at your college.
For reference point and calculate distance from college to home. In other case you can, take home as fixed point. And can measure the distance from home to college. In both the cases distance will be same. Hence you are free to take any point as reference point .
But condition is required fixed the origin point. So origin should not move. And this is called inertial frame of reference. So You must required, a frame of reference point to measure distance. Therefore without frame of reference you can’t calculate, any body or particle position on the Earth.
Also in universe, so in mathematics, you take x,y,z coordinate system, as frame of reference point. Its coordinate value taken as (0,0,0) at origin. It is always fixed to locate, any body or particle position. If once the body position is known. Then you can calculate distance or displacement of the body.
So distance gives magnitude of length. like 10 km, 20 km , 100 km … as in above figure shown .
Direction of Physical quantities : It can be in any direction. like left, right, up, down, at an angle. So its specify the particular direction of quantity. Therefore it is very important to know, the direction of physical quantity.
Otherwise you will not get the desired result. Suppose if you are moving. But your direction is not clear .Then you will not reach at your destination. Hence you need to understand vector and scalar quantities.
Vector quantities : It is that physical quantity. which has magnitude as well as direction . Because magnitude fixed the quantity and direction specify the quantity. Hence it also follow the triangle law of vector addition. So it is Compulsory to have magnitude and direction.
And its must follow vector addition law. Suppose on the office door . it is written pull. And you want to inter in the office. And if you are applying force and pushing the door. With a great force but you will be unable to open the door.
Therefore to open door you need force. And force is a vector quantity. Which has direction and magnitude both. So it is important to understand, you are applying force but in wrong direction. Hence you can’t open the door. So you have to apply the force in the right direction.
And right direction is pull. So direction is very very important for vector quantity. some examples of vector quantities, are force, displacement, velocity, acceleration, momentum, torque . And many more So direction is associated with Vector quantities.
Because without direction vector quantity will not specify. I hope you got. What is vector meaning ?
Scalar quantities : these are those quantities. which have only magnitude. But no direction and not follow triangle law of addition. Hence it has only and only magnitude. Take an example suppose in summer day. you are in a field. And you are told to ask the temperature. Which you are feeling.
So you may say hotter feeling 50⁰ C. In all direction of field. Because temperature has no any specific direction in field. So it is independent of direction. Now next example suppose in a sack 50 kg rice is filled. If i ask the mass of rice. you will say 50 kg. Alright but you will not say 50 kg in left or right And up, down.
Because it does not make any sense. So 50 kg rice in the sack is scalar quantity. Which are not associated with direction. Some examples of scalar quantities are, mass, temperature, time, distance, speed, work, power, energy. And many more. Also one more type of quantity, Which is called tensor. which you not need to study here. which is neither vector nor scalar.
suppose you want to write mass of rice = 50 kg . So for this you simply not write as much of language. Hence you actually use a symbol and write a = 50 kg. Where “a” represent mass of rice. Now take other example temperature of room = 30⁰ C. To represent this you write simply T = 30⁰ C .
Where T represent temperature of room generally. Therefore You use symbol for physical quantity representation. Because benefit of this is, only write short with symbol. So there all are example of scalar quantities. But for vector quantity see how you write ?.
→10 N c = 10 N towards right. Where c represent force you defined a symbol like →20 N towards right. d = 20 N towards right. But this type of writing is not good. Because vector quantity has direction and it is very important. Hence it is properties of vector quantity.
So you want to write vector quantity with some different symbol. Which can distinguish from other scalar quantity. And after seeing the symbol. You can well recognize that this is a vector quantity. As you know there are two type of quantity. One is called vector and other is scalar.
In similar way girls are of two type. One is married and other is unmarried. Therefore you easily recognize, Who is married girl. Who used vermilion is married girl. Hence for vector you use arrow symbol to recognize easily. This is vector quantity. Therefore vector is represented →
c = 20 N towards right .
💃 →20 N 10 N ←💃 💃
f₁ f₂ ↓ f₃
See here how we will write force for each case f₁, f₂, f₃ .
→ → →
f₁ = 20 N towards right , f₂ = 10 N towards left , f₃ = 5 N down.
Therefore important point, arrow above symbol indicate only about vector. Nothing about direction arrow always written above symbol. Always left to right. Whatever be the force direction. Its always written left to right. Remember never write right to left for vector representation.
Therefore arrow on symbol, indicate you are talking about vector does not gives direction . ← ↑
f₂ , f₃ f₃
if you write f = 10 N towards right. here 10 N represent magnitude and towards right direction.
There are many situation were you are only interested in magnitude. So in that case we write →⎟ f ⎥ = 20 N . This means you are only interested in magnitude, not considering direction. Therefore this can be also written as f = 20 N .So here arrow above symbol is removed only taking magnitude .
Some time we write vector as below
(Tail)p →→→→→→→→→→→→→→ q (head)
now we can represent as vector →
Here you can always write first tail .then head we can’t reverse. since direction always goes from tail to head .
What is vector position ?
Position : its mean where an object is located. Suppose in a cricket ground. Somebody ask you. Where is Sachin ? So its mean that, what is position of Sachin in cricket ground. Therefore somebody answer, position of Sachin is 5m from batting crease. What do you think, is this information is sufficient, for locating Sachin position in the ground. answer is big no. 💃
Because Sachin can be in any direction 5m from batting crease. So this information is insufficient to locate exact position of sachin. Therefore for exact position you must required direction. To locate exact position. Hence position is a vector quantity associated with direction .
If somebody ask, where is sachin in ground. And other person say sachin is 5m distance, Then this statement is also insufficient. Because from where he is 5m distance. So it may be from batting crease. from pavilion, from bowling point, from anywhere else. Now i hope, you got, what is vector position.
Hence you have to specify, from where he is 5m distance. If you say from batting crease then here batting crease is reference point. Therefore it is also called origin. So origin is required to talk about position. now position is vector quantity. Therefore you need its direction And take x-y axis.
now yo can locate any point on x-y plan. like point p and point q. opposite of x axis is negative and opposite of y axis is also negative. Therefore for position you subtract final position coordinate, minus initial position coordinate like x =x₂ – x₁ . y = y₂ – y₁
→ → →
r = (x₂ – x₁)i + (y₂ – y₁)j
Hope now your concept is clear. What is vector meaning for direction.
So this position is written in vector form. where r vector represent position. Because this will provide exact position of any body. or particle in plan . thanks for reading .What is vector meaning.
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