Answer
$\approx 0.0577$
Work Step by Step
Here, $u=\dfrac{v}{|v|}=\dfrac{\lt 2,2,-2 \gt}{\sqrt{2^2+2^2+(-2)^2}}$
or, $u=\lt \dfrac{1}{\sqrt 3},\dfrac{1}{\sqrt 3},\dfrac{-1}{\sqrt 3} \gt$
Now $df=(\nabla f (3,4, 12) \cdot u) ds$
or, $=[(\lt \dfrac{1}{\sqrt 3}\gt)(\lt \dfrac{1}{\sqrt 3},\dfrac{1}{\sqrt 3},\dfrac{-1}{\sqrt 3} \gt)](0.1)$
or, $=\dfrac{1}{\sqrt 3} (0.1)$
or, $\approx 0.0577$
