Question:
A vector field \(\vec p\) and a scalar field \(r\) are given by
\(\vec p=(2x^2-3xy+z^2)\hat i+(2y^2−3yz+x^2)\hat j+(2z^2−3xz+x^2)\hat k\)
\(r=6x^2+4y^2 - z^2-9xyz - 2xy + 3xz-yz\)
Consider the statements P and Q.
P: Curl of the gradient of the scalar field r is a null vector.
Q: Divergence of curl of the vector field p is zero.
Which one of the following options is CORRECT?
A vector field \(\vec p\) and a scalar field \(r\) are given by
\(\vec p=(2x^2-3xy+z^2)\hat i+(2y^2−3yz+x^2)\hat j+(2z^2−3xz+x^2)\hat k\)
\(r=6x^2+4y^2 - z^2-9xyz - 2xy + 3xz-yz\)
Consider the statements P and Q.
P: Curl of the gradient of the scalar field r is a null vector.
Q: Divergence of curl of the vector field p is zero.
Which one of the following options is CORRECT?
\(\vec p=(2x^2-3xy+z^2)\hat i+(2y^2−3yz+x^2)\hat j+(2z^2−3xz+x^2)\hat k\)
\(r=6x^2+4y^2 - z^2-9xyz - 2xy + 3xz-yz\)
Consider the statements P and Q.
P: Curl of the gradient of the scalar field r is a null vector.
Q: Divergence of curl of the vector field p is zero.
Which one of the following options is CORRECT?
Updated On: Feb 3, 2026
- Both P and Q are FALSE
- P is TRUE and Q is FALSE
- P is FALSE and Q is TRUE
- Both P and Q are TRUE
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The Correct Option is D
Solution and Explanation
The correct option is (D): Both P and Q are TRUE.
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