Advanced Engineering Mathematics
6th Edition
ISBN: 9781284105902
Author: Dennis G. Zill
Publisher: Jones & Bartlett Learning
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Chapter 9.13, Problem 29E
To determine
To find : the flux of
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(1) Is Mmxn (R) a vector space over the rational numbers Q? Explain.
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have it's curl identically equal to zero.
5. If vector T = (x + y +1)i + j - (x + y)k then T.curl(T )is
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- Which of the below graphs is of the following vector field? F(x, y) = xi + yj (A) -2 -4 -2 4 2.arrow_forward7.4 Let F(x,y,z)=(−7xz2,9xyz,−2xy3z)F(x,y,z)=(−7xz2,9xyz,−2xy3z) be a vector field and f(x,y,z)=x3y2zf(x,y,z)=x3y2z.∇f=(∇f=( , , )).∇×F=(∇×F=( , , )).F×∇f=(F×∇f=( , , )).F⋅∇f=F⋅∇f=arrow_forward4. If E and F are differentiable vector field, show that V(E × F) = F(V × E) – E(V × F).arrow_forward
- . Is it always true that T(0) = 0 where the zero vectors live in the appropriatespaces? Justifyarrow_forward1. Sketch, by hand, the following vector fields by sketching a few representative arrows: (a) F = (0, 1) (b) F = (0,x) (d) F = (y, - x) (c) F = X √x² + y² Y x² + y²arrow_forward9. Find the flux of the vector field B(x, y,z) shown in the left figure through the square S of side 2 shown in the right figure , oriented in the j direction, where B(x, v. z)== yi +xj x²+y² S + 2 1 3arrow_forward
- 1. Consider two vector fields: F1(x, y) = -yi+ xj and F2(7) = F. (a) Evaluate F and F, at the given points. (x, y) (1,0) (0, 1) (-1,0) (0, –1) F(r, y) F(1, y) (т, у) (1,1) (-1,1) (-1,–1) (1, –1) F(1, y) F(x, y) On the grids shown below, sketch above vectors of vector fields F (b) and F. F;(x, y) = -yi + xj F2(F) = F.arrow_forward3. Determine if the vector field F(x, y, z) = (y-z, x-z, x - y) is conservative or not.arrow_forward1. Consider the set of vectors S = {(1, 0, 0), (0, 1, 0)} and the field F = R of real numbers, then find the linear span L(S) of the vectors. What does it represents?arrow_forward
- H.W. draw the vector fields F(xy) = 2xi – yj F(xy) = xi – 3yj F(xy) = 2i – xj F(xy) = 2xi F(xy) = -yi 1. 2. %3D 3. 4. 5. %3Darrow_forward1. Let C₁ be the directed line segment that starts at (2,0) and ends at (-3,-5) and C₂ be the parabola with parametrization x = t, y = 4 - t² for t € [−3,2]. Let F be the vector field F(x, y) = (x² – 4y) î+ (2x + 3y²) î. F.dr. (a) Evaluate Sc₁ (b) Evaluate fF.dr where C is the positively oriented path consisting of the parabola y = 4-x² starting from (2,0) to (−3,−5) and the line segment from (-3, −5) back to (2,0). (c) Use the results in (a) and (b) to evaluate ſc₂ F · dr.arrow_forwardIn Problem 3, find the flux of the given vector field F through S according to the described orientation, where S is the portion of the cylinder of radius 2 centered along the z-axis that lies between the planes z = 0 and z = 3 in the first octant. The surface S is shown in the figure to the right. 3. F = yi+ 2x3+3zk, and S is oriented away from the z-axis.arrow_forward
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