F is the three-dimensional vector field defined by F(x,y,z) = ( z, x, y ). In other terms, P(x,y,z) = z, Q(x,y,z) = x, R( x,y,z) = y. Also, the domain T is the equilateral triangle in space with vertices (corners) at ( 2, 0, 0 ), ( 0, 2,0 ), ( 0, 0, 2 ), and normal vector n = ( a, b, c ) with a > 0 AND b > 0 AND c > 0. The boundary, or perimeter, C of the triangle T consists of three straight segments, oriented counterclockwise from (2,0,0) to (0,2,0), then from (0,2,0) to (0,0,2), and back from (0,0,2) to (2,0,0). Question: Calculate the circulation (line integral) of F around the boundary C of the triangle T.

F is the three-dimensional vector field defined by F(x,y,z) = ( z, x, y ). In other terms, P(x,y,z) = z, Q(x,y,z) = x, R( x,y,z) = y. Also, the domain T is the equilateral triangle in space with vertices (corners) at ( 2, 0, 0 ), ( 0, 2,0 ), ( 0, 0, 2 ), and normal vector n = ( a, b, c ) with a > 0 AND b > 0 AND c > 0. The boundary, or perimeter, C of the triangle T consists of three straight segments, oriented counterclockwise from (2,0,0) to (0,2,0), then from (0,2,0) to (0,0,2), and back from (0,0,2) to (2,0,0). Question: Calculate the circulation (line integral) of F around the boundary C of the triangle T.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.4: Linear Transformations

Problem 34EQ

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