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

question 15

Essay

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?

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Definitions:

Truth Table

A table used in logic to determine the validity of a proposition by listing all possible outcomes.

Modus Tollens (MT)

A logical rule stating that if a conditional statement (“if p then q”) is accepted, and the consequent (q) is denied, then the antecedent (p) must also be denied.

Modus Tollens (MT)

A logical argument form that asserts if a implies b, and not b is true, then not a must also be true.

Concordant Rates

In genetics, the likelihood of both members of a pair (especially twins) to either both exhibit or not exhibit a trait or disorder.