# Thread: Orthogonal Vectors

1. ## 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.

2. ## Re: Orthogonal Vectors

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