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Divergence & Curl Quizzes, Questions & Answers

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Divergence and curl are essential concepts in vector calculus, describing how vector fields expand, compress, and rotate in space. Divergence measures the net outflow from a point, identifying sources, sinks, or incompressible...

Questions: 15  |  Attempts: 10   |  Last updated: Dec 16, 2025
  • Sample Question
    Compute the curl of F(x,y,z) = <3x, 4y, 5z>.
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Divergence and curl are powerful tools in vector calculus that reveal how vector fields behave in space. Divergence measures the net flux emerging from a point, helping identify sources, sinks, or incompressible behavior. Curl,...

Questions: 15  |  Attempts: 10   |  Last updated: Dec 16, 2025
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    Which of the following is the correct formula for the divergence of a vector field F = <P, Q, R> in R³?
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Divergence and curl are fundamental tools in vector calculus, used to describe how vector fields behave in space. Divergence measures how much a field spreads outward from a point, indicating sources or sinks, while curl measures...

Questions: 15  |  Attempts: 10   |  Last updated: Dec 16, 2025
  • Sample Question
    Using the Del (nabla) operator ∇ = < ∂/∂x, ∂/∂y, ∂/∂z >, how is the divergence of a vector field F represented symbolically?
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Divergence and curl are central tools in vector calculus, revealing how vector fields behave in physical and mathematical systems. Divergence measures how much a field spreads outward from a point, identifying sources and sinks...

Questions: 15  |  Attempts: 10   |  Last updated: Dec 16, 2025
  • Sample Question
    Let F = < 3x, 5y, -2z > be a vector field representing the velocity of a fluid. Calculate the divergence of F.
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Divergence and curl are two of the most fundamental operators in vector calculus, revealing how vector fields behave in space. Divergence measures how much a field spreads out from—or converges into—a point,...

Questions: 15  |  Attempts: 10   |  Last updated: Dec 16, 2025
  • Sample Question
    What is the divergence of a vector field F = P i + Q j + R k in three dimensions?
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