Question

find the work done in the force camp F(x,y,z)=<xz,xy,zy> in a
particle that moves along the curve <t^2,-t^3,t^4> for 0
<= t <= 1

THE
F is F(x,y,z)= <xz,yx,zy>

Answer #1

Find the work done by the force field F(x,y,z)=6xi+6yj+7k on a
particle that moves along the helix r(t)=5cos(t)i+5sin(t)j+7tk, 0 ≤
t≤ 2π

Find the work done by the force ﬁeld F(x,y,z) = yz i + xz j + xy
k acting along the curve given by r(t) = t3 i + t2 j + tk from the
point (1,1,1) to the point (8,4,2).

Find the work done by the force field
F(x,y,z)=2xi+2yj+7kF(x,y,z)=2xi+2yj+7k
on a particle that moves along the helix
r(t)=3cos(t)i+3sin(t)j+4tk,0≤t≤2π

find the work done by the force field f(x,y)= <
x2+y2, -x > on a particle that moves along
the curve c: x2+y2=1, counterclockwise from
(0,1) to (-1,0)

Consider F and C below.
F(x, y,
z) = yz i +
xz j + (xy +
18z) k
C is the line segment from (1, 0, −3) to (4,
4, 1)
(a) Find a function f such that F =
∇f.
f(x, y,
z) =
(b) Use part (a) to evaluate
C
∇f · dr
along the given curve C.

Compute the work done by the force F= <sin(x+y), xy,
(x^2)z> in moving an object along the trajectory that
is the line segment from (1, 1, 1) to (2, 2, 2) followed
by the line segment from(2, 2, 2) to (−3, 6, 5) when force is
measured in Newtons and distance in meters.

Consider F and C below.
F(x, y, z) = yz i + xz j + (xy + 12z) k
C is the line segment from (2, 0, −3) to (4, 6, 3)
(a) Find a function f such that F =
∇f.
f(x, y, z) =
(b) Use part (a) to evaluate
C
∇f · dr along the given curve C.

Find the work done by the vector field F = 〈 2 xy + z/y , x^2 −
xz/ y^2 , x/y 〉 and C is the line segment that goes from (1,3,2) to
(1,4,6).

1. a) For the surface f(x, y, z) = xy + yz + xz = 3, find the
equation of the tangent plane at (1, 1, 1).
b) For the surface f(x, y, z) = xy + yz + xz = 3, find the
equation of the normal line to the surface at (1, 1, 1).

Using Stoke's Thm, find the work done by the vector field F(x,
y, z) = 〈z, x, y〉, that moves an object along the triangle with
vertices P(1, 0, 0), Q(0, 1, 0), R(0, 0, 1), in a counterclockwise
manner, starting and ending at P.

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