DotProduct

As of Version 9.0, vector analysis functionality is built into the Wolfram Language


gives the dot product of the two 3-vectors , in the default coordinate system.


gives the dot product of and in the coordinate system coordsys.

DetailsDetails

  • To use , you first need to load the Vector Analysis Package using Needs["VectorAnalysis`"].
  • is computed by converting and to Cartesian coordinates and then forming the dot product.

ExamplesExamplesopen allclose all

Basic Examples  (3)Basic Examples  (3)

In[1]:=
Click for copyable input

Dot product of two Cartesian vectors:

In[2]:=
Click for copyable input
In[3]:=
Click for copyable input
In[4]:=
Click for copyable input
Out[4]=
In[1]:=
Click for copyable input

Verify that a pair of vectors are orthogonal:

In[2]:=
Click for copyable input
In[3]:=
Click for copyable input
In[4]:=
Click for copyable input
Out[4]=
In[1]:=
Click for copyable input

Dot product of vectors in cylindrical coordinates:

In[2]:=
Click for copyable input
In[3]:=
Click for copyable input
In[4]:=
Click for copyable input
Out[4]=

Compare with the result from conversion to Cartesian coordinates:

In[5]:=
Click for copyable input
Out[5]=