# proove involving dot product and zero vector

• February 9th 2010, 04:34 PM
superdude
proove involving dot product and zero vector
Show that if $\vec u \cdot \vec v = \vec 0$ for all vectors $\vec v$ then $\vec u=\vec 0$
I know that 0 divided by v is 0, but how do I right that in terms of linear algebra?

It makes sense because any number multiplied with 0 will be 0, then it's just a sum of 0s, but I don't know how to give a formal proof
• February 9th 2010, 06:21 PM
Bruno J.
There is no statement. Your sentence makes as much sense as "If I take the bus."

Moreover, whatever you meant to say, you cannot divide by $\vec v$, it's a vector.
• February 10th 2010, 07:16 AM
Bruno J.
Hint : consider $\vec u \cdot \vec u$.