I F. dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = (x + y2)i + (y + z²)j + (z + x²)k, C is the triangle with vertices (4, 0, 0), (0, 4, 0), and (0, 0, 4). Step 1 Stokes' Theorem tells us that if C is the boundary curve of a surface S, then [ F. dr = £ £₂ curl F. ds. Since C is the triangle with vertices (4, 0, 0), (0, 4, 0), and (0, 0, 4), then we will take S to be the triangular region enclosed by C. The equation of the plane containing these three points is z = (-1)x+ (-1)y + ✓ Step 2 S is the portion of the plane z = 4 - x - y which lies over the region D in the xy-plane, where D is bounded by the x-axis, the y-axis, and the line y = (-1)x+ Step 3 For F(x, y, z) = (x + y²)i + (y + z²)j + (z + x²)k, we have curl F = (2=) i + -2x )j + (−2y )k. x Use Stokes' Theorem to evaluate

I F. dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = (x + y2)i + (y + z²)j + (z + x²)k, C is the triangle with vertices (4, 0, 0), (0, 4, 0), and (0, 0, 4). Step 1 Stokes' Theorem tells us that if C is the boundary curve of a surface S, then [ F. dr = £ £₂ curl F. ds. Since C is the triangle with vertices (4, 0, 0), (0, 4, 0), and (0, 0, 4), then we will take S to be the triangular region enclosed by C. The equation of the plane containing these three points is z = (-1)x+ (-1)y + ✓ Step 2 S is the portion of the plane z = 4 - x - y which lies over the region D in the xy-plane, where D is bounded by the x-axis, the y-axis, and the line y = (-1)x+ Step 3 For F(x, y, z) = (x + y²)i + (y + z²)j + (z + x²)k, we have curl F = (2=) i + -2x )j + (−2y )k. x Use Stokes' Theorem to evaluate

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.2: Determinants

Problem 13AEXP

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