With Vertices Of $( 0,0,0 ) , ( 6,6,6 )$

Multiple Choice

$\text { Let } \mathbf { F } ( x , y , z ) = \arctan \frac { x } { y } \mathbf { i } + \ln \sqrt { x ^ { 2 } + y ^ { 2 } } \mathbf { j } + \mathbf { k } \text { and let } C \text { be the triangle }$ with vertices of $( 0,0,0 ) , ( 6,6,6 )$ , and $( 0,0,12 )$ , oriented counterclockwise. Use Stokes's Theorem to evaluate $\int _ { c } \mathbf { F } \cdot d \mathbf { r }$ .

A) 0
B) 6
C) 9
D) 18
E) 12