Math Is Fun Forum

paulb203

Member

Registered: 2023-02-24

Posts: 136

Are vectors in maths like displacement in physics?

When encountering vectors in maths, at the introductory level at least, is it appropriate to think of them in terms of displacement?

Take a triangle ABC, with AC being the base

Vectors AB and BC added together give the resultant vector AC, yes?
(imagine arrows going to the right above AB etc)

But this doesn’t mean that the lengths of AB and BC added together equal the length of BC (the added lengths will be longer than BC),  yes?

What does it mean then?

Does it mean, or can it mean, the same as we’re taught in physics when dealing with displacement? The distance we end up from our point of origin A when we travel to C is the same regardless of whether we go directly to C, or via B?

So the distance covered going directly from A to C might be, say, 10m
And the distance going from A to C via B might be 12m

But the displacement is the same, i.e, 10m?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,169

Re: Are vectors in maths like displacement in physics?

Yes, that's right.  If you have vectors around a square then the sum is zero.  If you write the vectors as 2D components it is more obvious:

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

paulb203

Member

Registered: 2023-02-24

Posts: 136

Re: Are vectors in maths like displacement in physics?

Thanks, Bob.

That’s helpful; thinking of the vectors around a square adding to zero.

Although I’m slightly confused with your zeros and ones in brackets.

At first sight I thought they were column vectors (the top number meaning, ‘across’, the bottom number meaning, ‘up or down,’ relating to the x and y axis; and positive or negative before the value relating to right/left, up/down).

So I was expecting (1,0)(0,-1)(-1,0)(0,1).

But your numbers are (1,0)(0,1)(-1,0)(0,-1)

Do these amount to the same thing, or are you expressing this using a different method?

!! I think I might have it. I’ve imagined my origin as the top left of the square; have you imagined yours as the bottom left? I’ve started going across to the right, then down, etc. You, I think, have started going across to the left, then up, etc?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,169

Re: Are vectors in maths like displacement in physics?

Yes, they're the same thing. If you look at your vectors you'll see you've got the same ones; just in a different order so only the diagram is different.  I was imagining my square on a coordinate graph so x across and y up; but one of the useful things about vectors is it'll come out the same on any grid.

You can even have a grid based on axes at, say, 60 degrees so the usual squares become parallelograms.  All the usual results come out the same. (except maybe dot and cross products although you could probably find a way to include them)

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob