Explore Vector Calculus Identities 

Vector calculus identities are applied to inactive forms.

Create a generic gradient and curl.

In[1]:=

X grad = Inactive[Grad][f[x, y, z], {x, y, z}]

Out[1]=

In[2]:=

X curl = Inactive[Curl][{f[x, y, z], g[x, y, z], h[x, y, z]}, {x, y, z}]

Out[2]=

The divergence of any curl is zero.

In[3]:=

X Div[curl,{x, y, z}]

Out[3]=

The curl of any gradient is the zero vector.

In[4]:=

X \!\( \*SubscriptBox[\(\[Del]\), \({x, y, z}\)]\[Cross]grad\)

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