Consider the vector field F (x, y, z) = (2z + 3y) i+ (z + 3x)j+(y+ 2x) k. a) Find a functionf such that F = Vfand f(0, 0, 0) = 0. f(x, y, z) = b) Suppose C is any curve from (0, 0, 0) to (1, 1, 1) . Use part a) to compute the line integral

Q: c) Show that the vector field W(x, y, z) = (2yz+ xz – x², –2xz – yz + y?, y² – x² + z²) - - is a…

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Q: Find llFll and sketch several representative vectors in the vector field.

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Q: Consider the force field F(x, y) = (x, y). a) Sketch the vectors F(1,1), F(-2,1) and F(2,0) directly…

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Q: Find a vector perpendicular to the graph of 3(x – 9)2 + (y – 7)² = 13 – (z – 8)2 | at the point (10,…

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Q: Consider the vector field v(x)

A: Given, the vector field        v(x)=yx2+y2i^-xx2+y2j^+6k^                               ...(1)

Q: Let f(x,y,z) = x2 y−xy2+z3, P(1,1,2), u is the vector from P to Q(1, −2, −2). Determine the maximum…

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Q: Let f(x, y, z) = x²y - xy² + z³, P(1,1,2), u is the vector from P to Q(1, -2,-2). Determine the…

A: The given problem is to determine the maximum and minimum directional derivative of the given…

Q: Find a vector-valued function, using the given parameter, to represent the intersection of the…

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Q: Find r'(t), r(t), and r'(t) for the given value of to. Then sketch the space curve represented by…

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Q: 2. For the vector field F(x, y, z) = (x²y, xyz, −x²y²) F(x, y, z)=(x2y,xyz,-x2 y 2 ), find: (a) div…

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Q: Compute fa(P) where is a unit vector in the direction of . a) f(x, y) = x² + 2xy + 3y², P = (2,1), v…

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Q: For the vector-valued function r(t) = t³i + (2t² + 1)j + (3t − 6)k find the following and express…

A: According to bartleby guidelines we supposed to do the first three subparts of multiple subparts…

Q: Let f(x,y, z) = a² + 2y² +z² and g(x,y,z)=z-xy. Find a unit vector u satisfying D.f (1.1,2)= 0 = D,…

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Q: Prove that (Y - Y1)'(Y - Y1)= (-Y1)'(- Y1) + (Y-P)'(Y-P) where Y = n 1 Y and 1 is an n-dimensional…

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Q: Consider the vector field F = (2, -3). Let C be the straight line segment oriented from point (3,0)…

A: Given vector field, So,

Q: Q5) If the vector field T = (axy + Bz³)a, + (3x² – yz)a, + (3xz² – y)a, is irrotational, determine…

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Q: the vector fieldR-(x² 2 2 what is 282

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Q: Sketch the vector field. F(z, y) = (- 2 2 2 0 2 -2 0 -2 2 -2 2 -2 -2 2 -2 4- -4 -3 -2 -1 2 3 -2 -3-…

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Q: Sketch the vector field: F(x, y) = (1, 2y) Carefully draw at least four vectors in each of the four…

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Q: Find the curl of the vector field u = a) b) ▼xu =( V. (V x u) = = (7xyz², 6x² y³, 2x³ y³ z4 ).

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Q: Let C be the straight line segment in the xy-plane from the point (1, 2) to the point (5, 3). Let F…

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Q: For the vector field (x, y, z) evaluate the line integral along the curve made of three adjacent…

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