2. Which of the following statements are true for all vector fields, andwhich are true only for conservative vector fields?(a) The line integral along a path from P to Q does not depend onwhich path is chosen.(b) The line integral over an oriented curve C does not depend on howC is parametrized.(c) The line integral around a closed curve is zero.(d) The line integral changes sign if the orientation is reversed.(e) The line integral is equal to the difference of a potential functionat the two endpoints.(f) The line integral is equal to the integral of the tangential componentalong the curve.

according to our guidelines we can answer only three subparts and rest can be reposted.

Answered: 2. Which of the following statements…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.4: Spanning Sets And Linear Independence

Problem 76E: Let f1(x)=3x and f2(x)=|x|. Graph both functions on the interval 2x2. Show that these functions are...

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Let f1(x)=3x and f2(x)=|x|. Graph both functions on the interval 2x2. Show that these functions are linearly dependent in the vector space C[0,1], but linearly independent in C[1,1].
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2. A vector field is specified as G = 24xy ā, + 12(x² + 2)ā, + 18z²ā,. Given two points, P(1, 2, -1) and Q(-2, 1, 3), find: a. Gat P b. A unit vector in the direction of G at Q c. A unit vector directed from Q towardP
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The figure shows a vector field F and three paths from P (-3,0) to Q= (3,0). The top and bottom paths T and B comprise a circle, and the middle path M is a line segment. Determine whether the following quantities are positive, negative, or zero, or answer true or false. Be sure you can explain your answers. (Click on graph to enlarge) (a) F dr is ? (b) F- dř is ? F. dr is ? (c) F-dr is 2 () (e) ? v True or False: F- dr () ? v True or False F is a gradient field.
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