The given identities are verified by using operations of the del operator such as divergence and curl of the given vectors.
<h3>What are the divergence and curl of a vector field?</h3>
The del operator is used for finding the divergence and the curl of a vector field.
The del operator is given by 

Consider a vector field 
Then the divergence of the vector F is,
div F =  =
 = 
and the curl of the vector F is,
curl F =  =
 = 
<h3>Calculation:</h3>
The given vector fields are:
 and
 and 
1) Verifying the identity: 
Consider L.H.S
⇒ 
⇒ 
⇒ 
⇒ 
Applying the dot product between these two vectors,
⇒  ...(1)
 ...(1)
Consider R.H.S
⇒ 
So,

⇒ 

⇒ 
Then,

⇒  ...(2)
 ...(2)
From (1) and (2),

2) Verifying the identity: 
Consider L.H.S
⇒ 
⇒ 
⇒ 
Applying the cross product,
  ...(3)
 ...(3)
Consider R.H.S,
⇒ 
So,

⇒ 

⇒ 
Then,
 =
 =

...(4)
Thus, from (3) and (4),

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Disclaimer: The given question on the portal is incomplete. 
Question: Let  and
 and  be differential vector fields and let a and b arbitrary real constants. Verify the following identities.
 be differential vector fields and let a and b arbitrary real constants. Verify the following identities.
 