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Hello PF!

Prove the following: if u and v are two vectors in R

u[itex]\cdot[/itex]w - v[itex]\cdot[/itex]w = 0

w[itex]\cdot[/itex](u - v) = 0

I'm not sure what to do after applying the distributive property (in reverse). How do I go about proving that the vectors u and v are equal? I considered establishing two cases in which w = 0 and u-v = 0 but that doesn't help me out. Are there any properties that I can use to construct this proof?

## Homework Statement

Prove the following: if u and v are two vectors in R

^{n}such that u[itex]\cdot[/itex]w = v[itex]\cdot[/itex]w for all wεR^{n}, then we have u = v## Homework Equations

## The Attempt at a Solution

u[itex]\cdot[/itex]w - v[itex]\cdot[/itex]w = 0

w[itex]\cdot[/itex](u - v) = 0

I'm not sure what to do after applying the distributive property (in reverse). How do I go about proving that the vectors u and v are equal? I considered establishing two cases in which w = 0 and u-v = 0 but that doesn't help me out. Are there any properties that I can use to construct this proof?

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