Answer
$\approx 0.00076$ or, $\approx 0.0008$
Work Step by Step
Here, $u=\dfrac{v}{|v|}=\dfrac{\lt 3,6,-2 \gt}{\sqrt{3^2+6^2+(-2)^2}}$
or, $u=\lt \dfrac{3}{7},\dfrac{6}{7},\dfrac{-2}{7} \gt$
Now $df=(\nabla f (3,4, 12) \cdot u) ds$
or, $=[(\lt \dfrac{3}{169},\dfrac{4}{169},\dfrac{12}{169} \gt)(\lt \dfrac{3}{7},\dfrac{6}{7},\dfrac{-2}{7} \gt)](0.1)$
or, $=(\dfrac{9}{183})(\dfrac{1}{10})$
Thus, $\approx 0.00076$ or, $\approx 0.0008$
