Simple vector proof?

1. Nov 1, 2006

grimster

a is a vector and s and t are two integers. i'm supposed to show that:

sa+ta=(s+t)a

and

s*(ta)=(s*t)a

the two are so obvious i'm not sure how i prove them.

2. Nov 1, 2006

arildno

Make a careful check of the axioms given for your vector space, and see what needs to be proven.

3. Nov 1, 2006

grimster

thing is, i think i'm supposed to show it geometrically by drawing it. how do i do that?

4. Nov 1, 2006

*best&sweetest*

let a = (x,y) in the component form
then
sa+ta =
s(x,y) + t(x,y) =
(sx,sy) + (tx,ty)=
(sx+tx,sy+ty)=

(x(s+t),y(s+t))=

(s+t)(x,y)=
(s+t)a and do the similar for b)

5. Nov 1, 2006

arildno

Well, sa is parallell to a, isn't it?
And so is ta..
So, how would you geometrically add these vectors, and what resultant vector does this equal?

6. Nov 1, 2006

grimster

(s+t)*a

but that is what i'm supposed to show. so is it enough to just draw sa and then ta from where sa ends? add them together so to speak?

7. Nov 1, 2006

I guess so.

8. Nov 1, 2006

Office_Shredder

Staff Emeritus
That's about as geometrically proven as it gets....