Understanding Dot Product: Is v=w in Vectors?

[sjmacewan]

These vectors are giving me some real trouble...i'm fine with the in physics, but the math theory behind them is my weakness...

Ok, so we have that u.v=u.w where those are dot products of vectors. The question asks whether or not it makes sense to equate that to meaning that v=w.

Now, at first glance I would say yes. Since u never changes, for the dot product to be the same of the 2 expressions v and w would have to be the same vectors. But i have a strong feeling that I'm wrong...seems like one of those questions designed to make you second-guess yourself.

Any pointers on how to work this one out would be appreciated

 

[Reshma]

Hint: Dot product is commutative.

 

[sjmacewan]

hmmm, yes, i knew that; but I'm not entirely sure as to how that helps. It only seems to further my belief that v=w...which is possible i guess; maybe I'm overthinking it.

the way i see it is that if

u.v = u.w and
u.v = v.u

all that means is that v.u = u.w

and that doesn't get me any further to understanding :(

 

[matt grime]

u.v=u.w is the same as saying u.(v-w)=0. Now is it true that for all u, u.z=0 means z equals zero?

 

[sjmacewan]

As far as I know, no; that doesn't mean z=0. So v-w wouldn't have to be zero, meaning they're not equal :)

Thanks a lot! The commutativity hint was received poorly on my part, i never even considered taking u.w to the other side...