# Mathematica Calculus Help - Graphing Vectors

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 I cannot get the correct syntax for graphing these vectors Here's what I have. In[36]:= v = {2, 1, 0} w = {-1, -3, 1} Out[36]= {2, 1, 0} Out[37]= {-1, -3, 1} In[20]:= {-1, -3, 1} v.w Out[20]= {-1, -3, 1} In[22]:= -5 v\[Cross]w Out[22]= -5 Out[23]= {1, -2, -5} In[24]:= Sqrt[v.v] Out[24]= Sqrt[5] In[27]:= Sqrt[w.w] In[28]:= Sqrt[11] ArcCos[(v.w)/(Norm[v] Norm[w])] Out[28]= Sqrt[11] In[30]:= ArcCos[-Sqrt[(5/11)]] Out[30]= ArcCos[-Sqrt[(5/11)]] In[40]:= N[ArcCos[(v.w)/(Norm[v] Norm[w])]]/Degree Out[40]= 132.392 In[65]:= v = {1, 1, -2} w = {-1, -3, 1} Out[65]= {1, 1, -2} Out[66]= {-1, -3, 1} In[58]:= v.w In[67]:= -6 Out[67]= -6 In[68]:= v\[Cross]w Out[68]= {-5, 1, -2} In[69]:= Sqrt[v.v] Out[69]= Sqrt[6] In[70]:= Sqrt[w.w] In[75]:= Sqrt[11] N[ArcCos[(v.w)/(Norm[v] Norm[w])]]/Degree Out[75]= Sqrt[11] Out[76]= 137.608 In[131]:= Show[{vector3d[{0, 0, 0}, v], vector3d[{0, 0, 0}, w], vector3d[{0, 0, 0}, v\[Cross]w, 1]}, Axes -> True, PlotRange -> Automatic, BoxRatios -> Automatic, AxesLabel -> {"x", "y", "z"}, ViewPoint -> {6, 2, 2}] During evaluation of In[131]:= Show::gcomb: Could not combine the graphics objects in Show[{vector3d[{0,0,0},{1,1,1}],vector3d[{0,0,0},{2,2,2}],vector3d[{0,0,0},{0,0,0},1]},Axes->True,PlotRange->Automatic,BoxRatios->Automatic,AxesLabel->{x,y,z},ViewPoint->{6,2,2}]. >> Out[131]= Show[{vector3d[{0, 0, 0}, {1, 1, 1}], vector3d[{0, 0, 0}, {2, 2, 2}], vector3d[{0, 0, 0}, {0, 0, 0}, 1]}, Axes -> True, PlotRange -> Automatic, BoxRatios -> Automatic, AxesLabel -> {"x", "y", "z"}, ViewPoint -> {6, 2, 2}] Also how would I prove this? |v cross w| ^2 = |v|^2 |w|^2 - (v . w)^2 where v,w are arbitrary vectors in space Attachments:
 Show[{vector3d[{0, 0, 0}, v], vector3d[{0, 0, 0}, w], vector3d[{0, 0, 0}, v[Cross]w, 1]}, Axes -> True, PlotRange -> Automatic, BoxRatios -> Automatic, AxesLabel -> {"x", "y", "z"}, ViewPoint -> {6, 2, 2}] The above is wrong. There is no v[Cross]w syntax in Mathematica. Try Cross[v,w] Show[{vector3d[{0, 0, 0}, v], vector3d[{0, 0, 0}, w], vector3d[{0, 0, 0}, Cross[v,w], 1]}, Axes -> True, PlotRange -> Automatic, BoxRatios -> Automatic, AxesLabel -> {"x", "y", "z"}, ViewPoint -> {6, 2, 2}]