<s>[INST] Is there a counterexample to the claim that if $\mathbf y\cdot\mathbf y=1$ and $\mathbf x\cdot\mathbf y=c$ then $\mathbf x=c\mathbf y$? Let $x,y$ be arbitrary vectors where $\mathbf{y} \cdot \mathbf{y} = 1$ and $c$ be a real valued scalar. If 
$\mathbf{x} \cdot \mathbf{y} = c = c (\mathbf{y} \cdot \mathbf{y} ) = (c \mathbf{y} ) \cdot \mathbf{y} $, then
$\mathbf{x} = c \mathbf{y}$
Is this true? Feels like a sloppy conclusion no?
 [/INST] $\mathbf{x} = c \mathbf{y} + $ some vector perpendicular to $\mathbf{y}$
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