Question
Download Solution PDFA vector \(\vec{P}\) is given by \(\vec{P}\) = \(x^3 \vec{a_x}-x^2 y^2 \vec{a_y}-x^2 y z \vec{a_z}\). Which one of the following statements is correct?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven that,
\(\vec P = X^3 a_x - X^2y^2\vec A_y - X^2 YZ\vec a_z\)
Div\(\vec P = \frac{\partial} {\partial X} (x^3) - \frac{\partial}{\partial y}(x^2y^2) - \frac{\partial }{\partial z}(x^2yz)\)
= \(3x^2 -2X^2 - x^2y\)
=\(a_x (-X^2Z -0)- a_y (-2XYZ-0)+ a_z(-2xy^2-0)\)
\(\ne 0\)
\(\vec P\) is neither solenoidal nor irrotational.
Here, option 3 is correct.
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