You want to build a windmill at the origin that maximizes the circulation of the wind.The wind vector field at any point (x, y, z)in your coordinate world is given by $\vec { F } = ( y + 5 z ) \vec { i } + ( x - 2 z ) \vec { j } + ( 2 y - x ) \vec { k }$
(a)In which direction should you face the windmill to get maximum use from the wind?
(b)What will be the strength of the circulation of the wind when you face it in this direction?

Question

You want to build a windmill at the origin that maximizes the circulation of the wind.The wind vector field at any point (x, y, z)in your coordinate world is given by $\vec { F } = ( y + 5 z ) \vec { i } + ( x - 2 z ) \vec { j } + ( 2 y - x ) \vec { k }$ 
(a)In which direction should you face the windmill to get maximum use from the wind?
(b)What will be the strength of the circulation of the wind when you face it in this direction?

Quizplus · Accepted Answer

The Answer of You want to build a windmill at the origin that maximizes the circulation of the wind.The wind vector field at any point (x, y, z)in your coordinate world is given by $\vec { F } = ( y + 5 z ) \vec { i } + ( x - 2 z ) \vec { j } + ( 2 y - x ) \vec { k }$ 
(a)In which direction should you face the windmill to get maximum use from the wind?
(b)What will be the strength of the circulation of the wind when you face it in this direction?

You Want to Build a Windmill at the Origin That F⃗=(y+5z)i⃗+(x−2z)j⃗+(2y−x)k⃗\vec { F } = ( y + 5 z ) \vec { i } + ( x - 2 z ) \vec { j } + ( 2 y - x ) \vec { k }F=(y+5z)i+(x−2z)j​+(2y−x)k

You Want to Build a Windmill at the Origin That $\vec { F } = ( y + 5 z ) \vec { i } + ( x - 2 z ) \vec { j } + ( 2 y - x ) \vec { k }$