6. Consider the vector field F(x, y, z) = (y+ z)i+ (x+ z)j+(x+y)k. Compute the work done by the vector field along each of the following paths: (a) The curve r(t) = (t², t³, t+), for -1

6. Consider the vector field F(x, y, z) = (y+ z)i+ (x+ z)j+(x+y)k. Compute the<br>work done by the vector field along each of the following paths:<br>(a) The curve r(t) = (t², t³, t+), for -1 <t< 1.<br>(b) The line segment from (3, 1, 2) to (4,0, 5).<br>(c) The intersection of the cylinder x² + y? = a² and the plane x + y + z = d,<br>oriented counterclockwise.<br>

Extracted text: 6. Consider the vector field F(x, y, z) = (y+ z)i+ (x+ z)j+(x+y)k. Compute the work done by the vector field along each of the following paths: (a) The curve r(t) = (t², t³, t+), for -1 <>< 1.="" (b)="" the="" line="" segment="" from="" (3,="" 1,="" 2)="" to="" (4,0,="" 5).="" (c)="" the="" intersection="" of="" the="" cylinder="" x²="" +="" y?="a²" and="" the="" plane="" x="" +="" y="" +="" z="d," oriented="">

Jun 05, 2022

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6. Consider the vector field F(x, y, z) = (y+ z)i+ (x+ z)j+(x+y)k. Compute the work done by the vector field along each of the following paths: (a) The curve r(t) = (t², t³, t+), for -1

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