Find the General Form of the Equation of the Plane $$( - 1 , - 4 , - 2 ) , ( - 6,5,4 ) , ( 1 , - 2 , - 6 )$$

question 23

Multiple Choice

Find the general form of the equation of the plane passing through the three points. [Be sure to reduce the coefficients in your answer to lowest terms by dividing out any common factor.]
$$( - 1 , - 4 , - 2 ) , ( - 6,5,4 ) , ( 1 , - 2 , - 6 )$$

• A) \(12 x + 2 y + 7 z + 34 = 0\)
• B) \(12 x + 2 y + 7 z = 0\)
• C) \(x + 4 y + 2 z = 0\)
• D) \(12 x + 2 y + 7 z - 34 = 0\)
• E) \(x + 4 y + 2 z - 136 = 0\)

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Definitions:

Permanent Income Hypothesis

A theory suggesting that an individual's consumption at any given time is determined not just by current income but also by their longer-term income expectations.

Consumption

The action of using goods or services for personal use, satisfaction, or to fulfill needs.

Expected Income Stream

The anticipated series of payments received over time, often from investments, employment, or other sources of income.

Permanent Income Hypothesis

A theory suggesting that people's consumption choices are based on their long-term average income rather than their current income.