A conservative vector field is given by F=(-z-1)i + (-2y+2)j + (-z-1) k. Select two options that give a potential function for F Select one or more: U(z, y, z) = 2xz+x+3² − 2y+z DU(z,y,z)=x+2y+z U(z. y, z) = zz + x + y² − 2y + z U(x, y, z) = (x + 1) (z+1) – (z − 1) U(a, y, z)=(-2-1)-²-2y-z(-z-1) WINE

Q: 2. Sketch at least ten arrows in the vector field: F(x,y)=(-2y)i + (x+1)j

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Q: (5) Let V=R2. For (1, 1), (2, 32) EV and c ER, define addition and scalar multiplication operations…

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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: 4) Solve the following linear system or indicate the nonexistence of solution. X1 – 2x2 + 5x3 – 3x4…

A: Or, take x2 = k Hence, solution of the system is x1 = 1+2k, x2 = k, x3 = 1, x4 = 2

Q: 3. Prove that ox + 6x -4X12 is irreducible over Q.

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Q: Compute the vector assigned to the points P = (1, 1) and Q = (-3, -3) by the vector field F = (-y,…

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Q: If r(t) = u(t) x v(t), where u and v are the vector functions given below, find r'(2). u(2) = (6, 3,…

A: To find r'(2).

Q: 2. Find the gradient of the following scalar functions: a) T = 8/(x+y+2:²) b) V=3x²y³z c) U =…

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Q: Let r(t) = 5e7t + e2t and y(t) = 3e2t + 1le (i) Rewrite the given functions in the vector form Y(t)…

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Q: Determine the vector field of FF. F(x,y)=8i−4j

A: Solution

Q: Match the vector field with its graph. F(x, y) = yi 5 5 -5+ サ

A: To match the given vector field to its graph, where given graphs are given below.

Q: Q. (a) Find an equation of the tangent plane to each surface at the given point. (b) Find symmetric…

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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: -(4,2) use it to evaluate F. dr (1,0)

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Q: Find the gradient vector field (F(x, y, z)) of f(x, y, z) = √3x² + 4y² + 2². F(x, y, z) =

A: Solution:-

Q: The directional derivative of the field u(x, y, z) = x² – 3yz in the direction of the - vector (i +…

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

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Q: If the following vector function are equal to: A(t) = 5*t i + 2*t^2 j B(t) = 3*t^2 + 2 j Then…

A: The given problem is to find the derivative of the dot product of the two vector functions. Given…

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

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Q: reply as soon as posible.

A: To find out the conservative.

Q: Determine whether or not F(x,y) = (xy + y²,x² + 2xy) is a conservative vector field.

A: Given vector field is  Fx,y=xy+y2,x2+2xy Fx,y=F1,F2 A vector field is said to be conservative if…

Q: Michelle draws a restangle with a length of 6 cm. She draws a second rectangle with a length of 11…

A: Michelle draw 1st rectangle of length =6 cm 2nd rectangle=6+5=11cm And so on, she keep drawing more…