If $T (x, y, z) = x^{2} + y^{2} + 2 z^{2}$ defines the temperature at any location $(x, y, z)$ then the magnitude of the temperature gradient at point $P (1, 1, 1)$ is

2 \sqrt{6}

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4

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24

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\sqrt{6}

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Solution

The correct option is A $2 \sqrt{6}$
$g r a d T = \to ▽ T = 2 x^i + 2 y^j + 4 z^k$
So, $(g r a d T)_{P} = 2^i + 2^j + 4^k$
So, $| g r a d T |_{P} = \sqrt{4 + 4 + 16}$
$= \sqrt{24}$
$= 2 \sqrt{6}$

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