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
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