GATE (TF) Textile 2020 Question Paper Solution | GATE/2020/TF/15

Question 15 (Textile Engineering & Fibre Science)

If $F = xi + yj + zk$ , then the magnitude of $\nabla X F$ is __0__.

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$\nabla X F=(\frac{\delta f}{\delta x} i+\frac{\delta f}{\delta y} j+\frac{\delta f}{\delta y} k)\times(xi + yj + zk)$

$\nabla X F=\begin{bmatrix} i & j & k\\ \frac{\delta f}{\delta x} & \frac{\delta f}{\delta y} & \frac{\delta f}{\delta z}\\ x & y & z \end{bmatrix}$

$\left | \nabla X F \right |=i(\frac{\delta f}{\delta y} z-\frac{\delta f}{\delta z} y)-j(\frac{\delta f}{\delta x} z-\frac{\delta f}{\delta z} x)+k(\frac{\delta f}{\delta x} y-\frac{\delta f}{\delta y} x)$

$\left | \mode (\nabla X F) \right | =i(0-0)-j(0-0)+k(0)$

$\left | \nabla X F \right |=0$ (Ans)

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