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 July 29th, 2014, 11:21 AM #1 Member   Joined: Mar 2013 Posts: 71 Thanks: 4 prove that $x$ and $y$ are multiples Hellow! I've got the following problem: "Let $x,y \in \mathbb R^n$. If every $z \in \mathbb R^n$ which is orthogonal to $x$ is also orthogonal to $y$, prove that $x$ and $y$ are multiples". Proof: consider two vectors $x,y$. The projection of $y$ into $x$ is $w=\frac{x}{}$. Then we have $=0$. By hypothesis of the problem, $=0 \Rightarrow |y|^2=$. If I could get that $|x|^2|y|^2=^2$, it's done. But how?
 July 29th, 2014, 02:15 PM #2 Global Moderator   Joined: May 2007 Posts: 6,661 Thanks: 648 Let y = ax + z, where (x,z) = 0, with a = (x,y)/(x,x). However, since (x,z) = 0, then (y,z) = 0. Therefore (y,y) = [(x,y)]^2/(x,x), which is what you are trying to show. Thanks from walter r

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