What Value of the Constant a Makes the Vector Field $\mathbf { F } ( x , y , z ) = 2 x z \mathbf { i } + a y ^ { 2 } z \mathbf { j } + \left( x ^ { 2 } + y ^ { 3 } \right) \mathbf { k }$

question 56

Multiple Choice

What value of the constant a makes the vector field $\mathbf { F } ( x , y , z ) = 2 x z \mathbf { i } + a y ^ { 2 } z \mathbf { j } + \left( x ^ { 2 } + y ^ { 3 } \right) \mathbf { k }$ conservative?

• A) \(- 2\)
• B) \(- 1\)
• C)\(0\)
• D) \(1\)
• E) \(2\)
• F)\(3\)
• G) \(4\)
• H)\(5\)

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Annuitant

The individual who receives the benefits or payments from an annuity plan.

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A finance-related product that ensures a continual payment stream to a recipient, mainly used in planning for life after work.

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Steady cash flows facilitated at the decline of each era during a certain season.

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The rate of interest quoted on a loan or bond without adjusting for inflation or other factors that could affect the real rate of return.