Orthogonal Vectors

**iPod** · May 11th 2012, 11:59 AM

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.

**Plato** · May 11th 2012, 12:09 PM

Originally Posted by iPod

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 $3\left(\frac{a\times b}{\|a\times b\|}\right)$ .

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