title: Cross Product answer isn't correct?
body: <p>I'm having an issue with doing a function that takes 2 inputs: R (unit vector) and v (vector) and outputs a list of 3 vectors {vr,vp,vc}</p>
  <pre><code>vr = (v.R)R          
  vp = v-vr           
  vc = R*vp
  
  R = {0.36,0.48,0.8}
  v can equal i{1,0,0},j{0,1,0},k{0,0,1}
  </code></pre>
  <p>My issue is that with vc, it will give the incorrect answer at the position of the 1 in the v</p>
  <pre><code>  ``` 
     rotPrep[R_,v_]:= {Dot[v,R]R, v - Dot[v,R]R, Cross[R, v - Dot[v,R]R]};
  
     Print[&quot;{ir,ip,ic} = &quot;, rotPrep[R,i]];
  
     Print[&quot;{jr,jp,jc} = &quot;, rotPrep[R,j]];
  
     Print[&quot;{kr,kp,kc} = &quot;, rotPrep[R,k]];
  
    ```
  </code></pre>
  <p>I seem to have i right, but j and k gives me 1.9984x10^-17 in the position 1 was in.</p>
  <pre><code>   {ir,ip,ic} = {{0.1296,0.1728,0.288},{0.8704,-0.1728,-0.288},{0,0.8,-0.48}} 
     {jr,jp,jc} = {{0.1728,0.2304,0.384},{-0.1728,0.7696,-0.384},{-0.8,1.9984x10^-17,0.36}} 
     {kr,kp,kc} = {{0.288,0.384,0.64},{-0.288,-0.384,0.36},{0.48,-0.36,-1.9984x10^-17}} 
  
  </code></pre>