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Let $\mathbf { F } ( x , y , z ) = \left\langle \frac { z } { x - y } , \frac { z } { y - x } , \ln ( x - y ) \right\rangle$

Question 16

Multiple Choice

Let $\mathbf { F } ( x , y , z ) = \left\langle \frac { z } { x - y } , \frac { z } { y - x } , \ln ( x - y ) \right\rangle$ , find $\nabla \cdot ( \nabla \times \mathbf { F } )$ at the point $( 1,3,1 )$ .

A) $2$
B) $4$

C) $6$
D) $1$
E) $- 2$
F) $- 4$
G) $- 6$
H) $0$

Let F(x,y,z)=⟨zx−y,zy−x,ln⁡(x−y)⟩\mathbf { F } ( x , y , z ) = \left\langle \frac { z } { x - y } , \frac { z } { y - x } , \ln ( x - y ) \right\rangleF(x,y,z)=⟨x−yz​,y−xz​,ln(x−y)⟩

Multiple Choice

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Let $\mathbf { F } ( x , y , z ) = \left\langle \frac { z } { x - y } , \frac { z } { y - x } , \ln ( x - y ) \right\rangle$

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