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. Both P and Q are FALSE
• B. P is TRUE and Q is FALSE
• C. P is FALSE and Q is TRUE
• D. Both P and Q are TRUE

Answer 1

Answer: (D)

Both P and Q are TRUE

Answer 2

The correct option is (D): Both P and Q are TRUE.