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Vector Indentities

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Question 1

If f and g are scalar functions, which of the following is correct?

  • ∇(f + g) = ∇f − ∇g

  • ∇(f + g) = ∇f + ∇g

  • ∇(f + g) = f + g

  • ∇(f + g) = 0

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Question 2

For[Tex]\overrightarrow{F}[/Tex] = (y, −x, 0). compute ∇ ×[Tex] \overrightarrow{F}[/Tex] :

  • (0,0,−2)

  • (0,0,2)

  • (0,0,0)

  • (1,1,1)

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Question 3

Let [Tex]\overrightarrow{F}[/Tex] = (x,0,0), [Tex]\overrightarrow{G}[/Tex] = (0, y, 0). Find ∇. ([Tex]\overrightarrow{F}[/Tex] x [Tex]\overrightarrow{G}[/Tex]).

  • 1

  • 0

  • x + y

  • - 1

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Question 4

For f(x, y, z) = x2y+z3 find ∇2f.

  • 2y + 6z

  • 2y + 6z2

  • 2x + 3z2

  • 0

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Question 5

A vector field has zero divergence everywhere. Which is true?


  • Field has no sources or sinks

  • Field is constant

  • Field is zero

  • The field is a gradient


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There are 5 questions to complete.

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