Small vectors query (scalar product)

I have a short question to ask:

If  a, b and c are vectors,  and  a•b = c•b , is it absolutely correct so say a=c by comparison?

Student X

No. That is incorrect. Let me give you one simple counter-example:

[ Taking ( x, y, z) = x i + y j + z k  in general ]

Consider  a = ( 1, 0, 1)       b = (2, 1, 1)     c = ( 1, 1, 0) ,

While  a•b = c•b = 3,  clearly   a ≠ c.

Hope this clarifies. Peace.

Best Regards,

Mr Koh