3536 Use the result in Exercise 34(b). In each part, find the work done by the

Chapter 15, Problem 35

(choose chapter or problem)

Use the result in Exercise 34(b).

In each part, find the work done by the three-dimensional inverse-square field

\(F(r)=\frac{1}{\|r\|^{3}} r\)

on a particle that moves along the curve \(C\) .

(a)  \(C\) is the line segment from \(P(1,\ 1,\ 2)\) to \(Q(3,\ 2,\ 1)\) .

(b)  \(C\) is the curve

\(r(t)=\left(2t^2+1\right)i+\left(t^3+1\right)j+(2-\sqrt{t})k\)

where \(0 \leq t \leq 1\) .

(c) \(C\) is the circle in the \(xy\)-plane of radius 1 centered at \((2,\ 0,\ 0)\) traversed counterclockwise.

Equation Transcription:

Text Transcription:

Equation Transcription:

F(r) = frac 1 / ||r||^3 r

C

C

P(1, 1, 2)

Q(3, 2, 1)

C

r(t)=(2t^2 +1)i + (t^3 +1)j + (2 − sqrt t)k

0 leq t leq 1

C

xy

(2, 0, 0)