Why could we represent the addition of two vectors like this?

[parshyaa]

Do we have any proof to show that we can represent the addition of two vectors like this, i mean do we have proof for triangle law of vector addition(or its a law that is why we can't have its proof, then please give me a satisfying reason for this)

 

[Chestermiller]

Do we have any proof to show that we can represent the addition of two vectors like this, i mean do we have proof for triangle law of vector addition(or its a law that is why we can't have its proof, then please give me a satisfying reason for this)
View attachment 211264

What is your guess?

 

[Nugatory]

It's a definition: Vectors are mathematical objects that add that way.

It turns out that these mathematical objects are useful, so we use them.

 

[parshyaa]

What is your guess?

I have a explanation(but its wrong), i think more precisely a vector addition can be represented like this

Because when we hit a pencil box we get something like this(when we hit it from left side and then from right side and the we hit it from left and right side together)

And as we know that vectors can be shifted parallely then we can shift B to the head of A then we would get something we were proving, but as size of vector represents magnitude we are not shure that triangle would form or not.

 

[jtbell]

The "head to tail" and "tail to tail" vector diagrams are equivalent representations of the "parallelogram rule" for vector addition. This is a mathematical statement. The physics comes in when we observe experimentally that forces obey this rule, and therefore we can use vectors to represent forces.

The parallelogram rule (applied to forces) goes all the way back to Newton. See Corollary I of his Principia Mathematica.