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MVC SHOW ALL WORK!! Chapter 3 Quiz NAME: #1. Let f be a scalar field and F a vector field. Indicate which of the following are scalar fields (S), vector fields (V), or meaningless (M). a. div f b. f c. F d. div( f ) e. curl( f ) f. (div F) g. curl(curl F) h. div(div F) i. ( f ) j. div(curl( f )) k. curl(div( f )) #2. Let r ( x, y, z ) and let r denote r . Verify that (ln r ) MVC r . r2 #3 Determine whether the path x (t ) (et cos t , et (sin t cos t ), et sin t ) is a flow line for the vector field F ( x z , 2 x, y ) . #4 Explain why F x, y, z 2 xy z i x 2 y j x yz 1 k cannot be the gradient of some scalar field f without mentioning curl. (That is, show that there is no scalar function f such that F f ?). MVC 1 #5. Calculate the flow line x (t ) of the vector field F ( x, y ) x 2 , 2 that passes through the point y (1,3) at t = 1. (That is, x (1) (1,3) ) MVC #6 Suppose F x, y, z 2 xy z i x 2 y j x 1 k . Determine whether or not F is a conservative vector field (i.e. is there a scalar function f such that F f ?). If it is, find the function f for which F f . If not, explain clearly. MVC