a. Find dr for the path r(t) = g(t)i + h(t)j + k(1)k. b. Evaluate the force F along the path. c. Evaluate F• dr. 63. F = xyºi + 3x(xy³ + 2)j; r(t) = (2 cos t)i + (sin t)j, 0

a. Find dr for the path r(t) = g(t)i + h(t)j + k(1)k.<br>b. Evaluate the force F along the path.<br>c. Evaluate<br>F• dr.<br>63. F = xyºi + 3x(xy³ + 2)j; r(t) =<br>(2 cos t)i + (sin t)j,<br>0 <t< 27<br>3<br>j; r(t) = (cos t)i + (sin t)j,<br>1 + y?<br>64. F<br>1 + x?<br>0 <t< T<br>65. F = (y + yz cos xyz)i + (x² + xz cos xryz)j +<br>(z + xy cos xyz)k; r(t) = (2cos t)i + (3 sin t)j + k,<br>0 <t< 2m<br>66. F = 2xyi – y²j + ze*k; r(t) = –ti + Vtj + 3tk,<br>1<t< 4<br>67. F = (2y + sin x)i + (z² + (1/3)cos y)j + x*k;<br>r(t) = (sin t)i + (cos t)j + (sin 2t)k, -7/2 < i </2<br>68. F = (x²y)i +<br>rj + xyk; r(f) = (cos t)i + (sin t)j +<br>(2 sin² t – 1)k, 0<t< 2m<br>

Extracted text: a. Find dr for the path r(t) = g(t)i + h(t)j + k(1)k. b. Evaluate the force F along the path. c. Evaluate F• dr. 63. F = xyºi + 3x(xy³ + 2)j; r(t) = (2 cos t)i + (sin t)j, 0 <>< 27="" 3="" j;="" r(t)="(cos" t)i="" +="" (sin="" t)j,="" 1="" +="" y?="" 64.="" f="" 1="" +="" x?="" 0=""><>< t="" 65.="" f="(y" +="" yz="" cos="" xyz)i="" +="" (x²="" +="" xz="" cos="" xryz)j="" +="" (z="" +="" xy="" cos="" xyz)k;="" r(t)="(2cos" t)i="" +="" (3="" sin="" t)j="" +="" k,="" 0=""><>< 2m="" 66.="" f="2xyi" –="" y²j="" +="" ze*k;="" r(t)="–ti" +="" vtj="" +="" 3tk,=""><>< 4="" 67.="" f="(2y" +="" sin="" x)i="" +="" (z²="" +="" (1/3)cos="" y)j="" +="" x*k;="" r(t)="(sin" t)i="" +="" (cos="" t)j="" +="" (sin="" 2t)k,="" -7/2="">< i i="">

Jun 04, 2022

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a. Find dr for the path r(t) = g(t)i + h(t)j + k(1)k. b. Evaluate the force F along the path. c. Evaluate F• dr. 63. F = xyºi + 3x(xy³ + 2)j; r(t) = (2 cos t)i + (sin t)j, 0

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