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For problems 5 - 11 find the potential function for the vector field. 5. F =...
2. a) Find a potential of the vector field f(x, y) = (a2 +2xy - y2, a2 - 2ry - y2) b) Show that the vector field (e" (sin ry + ycos xy) +2x - 2z, xe" cos ry2y, 1 - 2x) is conservative.
Consider the following potential function. a. Find the associated gradient field F =Vo. b. Sketch three equipotential curves of Q. c. Show that the vector field F is orthogonal to the equipotential curve at all points (x, y). 5) (12 points) $(x, y) = 2x² + 2y2
7. The vector field F =< 3x2z In y + ze+2 +20, - 3y?, x° In y + ce2 +423 > is conservative. Find a potential function f(x, y, z) such that F=Vf. Y
Vector field F = î 3y + ŷ (5 – 2x) + î (22 – 2) is given. Find: (e) The surface integral of the normal component of the curl of F over the open hemisphere x + y2 + z = 4 above the x-y plane.
is a conservative vector field (on its implied domain) a. Find its potential function b. Find where C is the curve shown below and given by the vector equation Solve using concepts of Vector Fields, Line Integrals, and/or The Fundamental Theorem for Line Integrals. +sec2 F dr (sin-t-2, cos-t-2, cos(nt) 式t) 3 2 2 1 2 1 0 2 +sec2 F dr (sin-t-2, cos-t-2, cos(nt) 式t) 3 2 2 1 2 1 0 2
can you solve this vector problems? Find the outward flux of the vector field F(x, y, z) = (xi + yj + zk)/(x 2 + y 2 + z 2 ) 3/2 across the ellipsoid 4x^2 + 9y^2 + z^2 = 1. 6. (12 pts.) Find the outward flux of the vector field F(r,y, ) (ri yj+ zk)/(x2 + y2 22)3/2 across the ellipsoid 4r2 +9y2 + z2 = 1 6. (12 pts.) Find the outward flux of the vector...
Decide whether or not the vector field is a gradient field (i.e. is conservative). If it is conservative, find a potential function. (ii) F(x,y)-6ญ่-12xVJ (iv) F(x, y, z)-< ye", e + z,y > Decide whether or not the vector field is a gradient field (i.e. is conservative). If it is conservative, find a potential function. (ii) F(x,y)-6ญ่-12xVJ (iv) F(x, y, z)-
D Question 11 12 pts to Consider the vector field F (x, y, z) =< 2x – yz, 2y – az,2z – xy>. a) (3) Is this vector field conservative? Justify your answer. b) (9) Find the amount of work done by this vector field in moving a particle along the curve (t) =< 3cost, cos’t, cos” (2t) > from t = 0 tot = 1
Find the potential function f for the field F. F= 을 시
please answer asap (it is all the professor asked) (5) Consider the gradient vector field F ▽f where f(x,y) = cos(2x-3y). Find curves G and C2 that are not closed such that JG F·dr = 0 and 1, F . dr-1. Explain why you pick the curve you do, and how you know the integrals have the correct values. (Hint: Try picking a straight line between the origin and some simple point (a, b) that you choose later.) (5) Consider...