Use Stokes' Theorem to evaluate F. dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = I + (x + yz)j + (xy – Vz)k, C is the boundary of the part of the plane 5x + 4y + z = 1 in the first octant.

Evaluate F-dī where F(x, y, z)=li +(x+yz)j+(xy-Vz )k and C is the boundary of the part of the plane 3x+2y+z=6 in the first octant. C is a positively oriented curve.

AM (2) - Edited Let W be the plane with equation x + 2y + 2z = 1. Define the function f (x,y, z) to be f(x, y, z) = distance from (x, y, z) to W. %3D (a) For each real number k > 0, the level surface f(x, Y, z) = k can be described in terms of other familiar surfaces. Give a geometric description of the level surface f(x, y, z) = k. Be as precise as possible when explaining your answer. %3D (b) For each real number k > 0, produce an explicit equation for the level surface f(r, y, z) = k. (c) Consider the function g = f² (distance square). Find the partial derivatives (r, y, z) and Buể (T, y, z). What do you notice? (d) Let F(t) be a single-variable function. The following table gives some relevant values of this function. F F' F" t = 0 -4 10 t = 1 13 -1 t = 2 -2 9. -3 82h aydz Suppose that h(x, y, z) = F(g(x, Y, z)). Find values of (0,0, 2) and (0, 0, 2) 3:07 7 days ago Dreamland Glass Animals 3:21 Dreamland Glass Animals The Score (Expanded Editi Fugees ADE 7 days ago 3:59 Heat Waves…

4. Find the point of intersection (if any) of the line with parametric equations x = 1+2t, y = -1+t, and z = 2+3t and the plane 2x + 3y – 4z = 6* - u dod ot lenogo