Let $\vec { F } = \left( - 2 x ^ { 2 } - a x z \right) \vec { i } + \left( b x ^ { 2 } + 16 \right) \vec { j } + ( x + c y ) \vec { k }$

question 4

Short Answer

Let $\vec { F } = \left( - 2 x ^ { 2 } - a x z \right) \vec { i } + \left( b x ^ { 2 } + 16 \right) \vec { j } + ( x + c y ) \vec { k }$ be a smooth vector field with $\operatorname { curl } \overrightarrow { \vec { F } } ( 1 , - 4,4 ) = - 3 \vec { i } + 3 \vec { j } + 8 \vec { k }$ Determine the values of a, b and c.

---

Definitions:

Second-Bidder

Refers to the auction bidder with the second-highest bid, often relevant in Vickrey auctions where this bidder's price determines the sale price.

Vickrey Auction

A sealed-bid auction where the highest bidder wins but pays the second-highest bid, encouraging true value bids.

English Auction

A type of auction where the price ascends and participants openly bid against each other, with the highest bid at the close of the auction winning.

Reservation Price

The utmost price a buyer is ready to offer for a good or service.