curl(V) = 7*V = (01,02,03)X(V1,V2,V3) := ei(@2v3 —@3V2)+e2(@3v1 –O1v3)+e3(@iv2-02vi) for any vectorfield V = viei +...

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curl(V) = 7*V = (01,02,03)X(V1,V2,V3) := ei(@2v3 —@3V2)+e2(@3v1 –O1v3)+e3(@iv2-02vi) for any vectorfield V = viei + v2e2 + v3

Problem 0.2. Show that curl(grad(f)) = 5xOf=0 for any smooth function fon R CR3.

Answer 1

Answer #1

Answer: Here we have to show that curl (grad of)=0 be vx10f)=0. 1. By the definition of of, (gradf) - grad f= of it af J + af

Answer 2

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curl(V) = 7*V = (01,02,03)X(V1,V2,V3) := ei(@2v3 —@3V2)+e2(@3v1 –O1v3)+e3(@iv2-02vi) for any vectorfield V = viei +...

curl(V) = 7*V = (01,02,03)X(V1,V2,V3) := ei(@2v3 —@3V2)+e2(@3v1 –O1v3)+e3(@iv2-02vi) for any vectorfield V = viei + v2e2 + v3e3 on R. Problem 0.1. Compute curl(V) = V x V for the following vectorfields on R’: • V = (x283, X1X3, X122) = x2x3e1 + x113€2 + x1x203; • V = (2x3, 5x1, 4x2) = 2x3e1 + 5x1e2 + 4x203; • V = f(a,b,c) * (21, 22, 23) = A xx, where A = (a, b, c) = ae +bez +...
Consider the following graph. V(G) = {v1, v2, v3, v4}, e(G) = {e1, e2, e3, e4,...

Consider the following graph. V(G) = {v1, v2, v3, v4}, e(G) = {e1, e2, e3, e4, e5}, E(G) = {(e1,[v1,v2]),(e2,[v2,v3]),(e3,[v3,v4]), (e4, (v4,v1)), (e5,[v1,v3])} Draw a picture of the graph on scratch paper to help you answer the following two questions. How many edges are in a spanning tree for graph G? What is the weight of a minimum-weight spanning tree for the graph G if the weight of an edge is defined to be W (ei) L]?