What is a Vector ?

Concept behind it!!!A quantity having direction as well as magnitude, especially as determining the position of one point in space relative to another.

The definition is for people who already know what it is and doesn’t explain what they are…

Why we use them?

The vectors came into existence just to give more accurate information about things when there is more than one information involved.Keep it in Mind as we go forward.

Let’s Understand it

Let’s say you are standing at the back of your car with a Box in your hand and you have 8 tasty Apples 🍏 in it. You see your friend standing at the front door of your car. He says…

Your Hungry friend asks: How many Apples do you have in that Box?You Say(without lying): There are 8 Apples in the Box.

Note that the answer “There are 8 Apples in the Box” gives the complete information about the Box.

Therefore, the number 8 itself represents the complete state of the Box and there is no need of any other info.,so we call it a Scalar Quantity.

Let’s consider you have a different Box.

and the Box contains 4 tasty Apples 🍏 & 3 Oranges.

Your Hungry friend asks: How many Apples do you have in that Box?You Say(without lying): There are 4 Apples in the Box.

Even though you have given the correct information. It does not represent the complete state of the Box.

The problem is that you cannot represent the state of the Box just by using a single fruit. Both the statements

The Box contains 4 Apples.

or

The Box contains 4 Oranges.

are correct but they does not represent the complete state of the Box completely.

You can represent the state of the Box and give the complete information about the Box by writing it like this:

Box = [4                 //where Apples=4       3]                //and Oranges=3

which tells us,

Vectors are basically a List of Numbers.

The above statement is Correct, usually used in computer science and works perfectly also it doesn’t support the first definition completely.

So,What about the direction and the magnitude of Vectors?

To understand it further in terms of direction. Let’s consider the same example with a different physics angle.

Your Hungry friend knows about the box and now he is coming towards you. He takes 4 Steps along the car and takes 3 more towards you.

Save your Fruits

Now, you can represent those steps into a vector like this:

Steps = [ 4                              //Steps along the car          3 ]                           // towards you

2D Vector

And use the Pythagoras theorem to calculate the vector.

√(4²+3²)

where 5 is the magnitude and AB (arrow) representing the direction of the Vector. Hence,

Vector can be represented by a single quantity having direction as well as magnitude.

Also, same can be done for 3D Space to get 3D vector and many more.

You can do vice-versa and say, for the vectorThe X-component of the Vector is 3 &The Y-component of the Vector is 4.

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