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Let F\vec { F } Be a Constant Vector Field With F=ai+bj+ck { \vec { F } } = a \vec { i } + b \vec { j } + c \vec { k }

question 43

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Let F\vec { F } be a constant vector field with F=ai+bj+ck { \vec { F } } = a \vec { i } + b \vec { j } + c \vec { k } , where a, b, c are constants satisfying the condition a2+b2+c2=1a ^ { 2 } + b ^ { 2 } + c ^ { 2 } = 1 .Let S be a surface lying on the plane x + 4y - 5z = 10 oriented upward.
If the surface area of S is 10, what is the smallest possible value of SFdA\int _ { S } \vec { F } \cdot \vec { d A } , and what are the corresponding values of a, b, c?

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Definitions:

Trial Balance

A bookkeeping report that lists the balances of all ledgers accounts to check that debits equal credits in the double-entry accounting system.

Debits

Debits refer to an accounting entry that results in either an increase in assets or expenses or a decrease in liabilities or equity on a company's balance sheet.

Ledger

A Ledger is a book or collection of accounts in which account transactions are recorded, classified, and summarized.

Wages Expense

The total cost incurred by a company for paying its employees, including salaries, wages, and other forms of compensation.

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