Let $\vec { a } = a _ { 1 } \vec { i } + \alpha _ { 2 } \vec { i } + \alpha _ { 3 } \vec { i }$

question 40

Multiple Choice

Let $\vec { a } = a _ { 1 } \vec { i } + \alpha _ { 2 } \vec { i } + \alpha _ { 3 } \vec { i }$ be a constant vector and f(x, y, z) be a smooth function.Which statement is true?

• A)If \(\operatorname { div } f \vec { a }\) is a divergence free vector field then\(\nabla\)f is parallel to
• \(\vec { \alpha }\)
• B)If \(\operatorname { div } f \vec { a }\) is not a divergence free vector field then \(\nabla\)f is perpendicular to
• \(\vec { \alpha }\)
• C)If \(\operatorname { div } f \vec { a }\) is a divergence free vector field then \(\nabla\)f is perpendicular to
• \(\vec { \alpha }\)
• D)If \(\operatorname { div } f \vec { a }\) is not a divergence free vector field then \(\nabla\)f is parallel to
• \(\vec { \alpha }\)
• E)If \(\operatorname { div } f \vec { a }\) is a divergence free vector field then \(\nabla\)f is constant.

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Face Saving

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The false belief that resources or benefits must be divided in a zero-sum manner, where one party's gain is another's loss.

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