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Math Help - Orthogonal Vectors

  1. #1
    Member iPod's Avatar
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    Orthogonal Vectors

    If \textbf{a}=2\textbf{i}-\textbf{j}+2\textbf{k} and \textbf{b}=\textbf{i}+3\textbf{j}-\textbf{k}, find a vector of magnitude \textbf{3} which is orthogonal to both \textbf{a} and \textbf{b}.

    So far I have only calulated two dot products from an arbitrary vector however I'm not too sure what to do afterwards.
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  2. #2
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    Re: Orthogonal Vectors

    Quote Originally Posted by iPod View Post
    If \textbf{a}=2\textbf{i}-\textbf{j}+2\textbf{k} and \textbf{b}=\textbf{i}+3\textbf{j}-\textbf{k}, find a vector of magnitude \textbf{3} which is orthogonal to both \textbf{a} and \textbf{b}.
    The answer is 3\left(\frac{a\times b}{\|a\times b\|}\right).
    Last edited by Plato; May 11th 2012 at 01:11 PM.
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