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)\(5\)

---

Definitions:

Honesty in Fact

A concept referring to the genuine intention or belief without intent to deceive in transactions or dealings.

Conform to Contract

The requirement that goods or services supplied under a contract must meet the specifications agreed upon in the contract.

Substitute Goods

Products or services that can be used in place of one another, offering consumers alternatives.

Risk of Loss

Risk of loss refers to the legal and financial responsibility for damages, destruction, or loss of property, often determining who bears this risk during transactions or in the event of unforeseeable incidents.