Explain why or why not Determine whether the following statements are true and give an explanation or counterexample. a. For a function f of a single variable, if f ′( x ) = 0 for all x in the domain, then f is a constant function. If ▿ ·F = 0 for all points in the domain, then F is constant. b. If ▿ × F = 0 , then F is constant. c. A vector field consisting of parallel vectors has zero curl. d. A vector field consisting of parallel vectors has zero divergence. e. curl F is orthogonal to F .
Explain why or why not Determine whether the following statements are true and give an explanation or counterexample. a. For a function f of a single variable, if f ′( x ) = 0 for all x in the domain, then f is a constant function. If ▿ ·F = 0 for all points in the domain, then F is constant. b. If ▿ × F = 0 , then F is constant. c. A vector field consisting of parallel vectors has zero curl. d. A vector field consisting of parallel vectors has zero divergence. e. curl F is orthogonal to F .
Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.
a. For a function f of a single variable, if f′(x) = 0 for all x in the domain, then f is a constant function. If ▿ ·F = 0 for all points in the domain, then F is constant.
b. If ▿ × F = 0, then F is constant.
c. A vector field consisting of parallel vectors has zero curl.
d. A vector field consisting of parallel vectors has zero divergence.
e. curl F is orthogonal to F.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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