3. Consider the vector field F(r, y, z) = (2ry, x² + 2yz, y²). a) Show that curlF = (0,0,0). b) The result (a) implies that F is conservative. Compute a potential function f of F. c) Using the results from part a), from part b) and the fundamental theorem of line integrals in a vector field (and only these three), compute the line integral over the vector field F along any possible smooth curve C from (1,-3,2) to (3,2,-1) .

3. Consider the vector field F(r, y, z) = (2ry, x² + 2yz, y²). a) Show that curlF = (0,0,0). b) The result (a) implies that F is conservative. Compute a potential function f of F. c) Using the results from part a), from part b) and the fundamental theorem of line integrals in a vector field (and only these three), compute the line integral over the vector field F along any possible smooth curve C from (1,-3,2) to (3,2,-1) .

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.1: Inner Product Spaces

Problem 12EQ

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