Solve the Problem $\mathbf { F } = \mathrm { x } ^ { 5 } \mathrm { y } ^ { 4 } \mathbf { i } + 9 \mathrm { z } ^ { 2 } \mathbf { j } + \mathrm { z } \mathbf { k }$

Solve the problem.
-Consider a fluid with a flow field $\mathbf { F } = \mathrm { x } ^ { 5 } \mathrm { y } ^ { 4 } \mathbf { i } + 9 \mathrm { z } ^ { 2 } \mathbf { j } + \mathrm { z } \mathbf { k }$ . A miniature paddlewheel (idealized) is to be inserted into the flow at the point $( 1,1,1 )$ . Find a vector describing the orientation of the paddlewheel axis which produces the maximum rotational speed.