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I have a question today about vectors: suppose we are asked find unknown $x$ coordinates of two vectors which are directed opposite sides, so for example one vector $a$ is vector such that
$a=(x,3)$ and second vector $b=(8,x)$ our task is to find $x$ please help me, I have a national exam in one week and meet such problem in the exam textbook. Please give me idea how to solve such vector related problems

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Directed opposite sides means that there exists $k$ such that $ka=b$ and $k<0$. You get the equations $kx=8; 3k=x$. From here, find $k$ and pick the negative solution. From there, find $x$.

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thanks very much –  dato datuashvili Jul 8 '11 at 7:16

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