S,F•dr, and C is the triangle, with Use Stokes Theorem to evaluate where F(x,y; =) = (x+ y² )i+ (vy+ =²)j+(=+x²)k vertices(1,0,0),(0,1,0) and (0,0,1) (Orientation of C should be counterclockwise when viewed from above).

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A: our objective is to find the equation of plane.

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Q: 2) = ( (x, y, z) =

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Q: Consider the simple lincar model Y, = Be + B,x, + C. where -N(0,0²); i= 1,2, --,n. 1. Show that a)…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts(a, b-i,…

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Q: 3) Consider stress of a body at a particular point is give in the form of Q(x1, x2, X3) = xỉ – x –…

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Q: The following r(t) = (3 sint, 4 cost) represents vector-valued function. i) ii) iii) By eliminating…

A: The followingr(t)=(3sint,4 lcost) represents vector-valued function.i) By eliminating parameter 1,…

Q: Let P denote the path that goes in straight lines from (0,0, 2) to (0,1, 2) to (1,1, 2) to (1,0, 2)…

A: Given: F→(x, y, z)=(1-z)5yxez-2z15+14

Q: 10. Find an equation of the plane that passes through the points (x, y, z) = (1, 2, −1), (x, y, z) =…

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Q: -}]-=[}]»=[}- [] 3 Find Let vị = and p = 3 a hyperplane [f: d] (in this case, a line) that strictly…

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Q: W(s, t) = F(u(s, t), v(s, t)), where F, u, and u are differentiable. If u(-6,0) = 6, u,(-6,0) = -2,…

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Q: Line. O Find Hhe least (0,0) , (1,1) square 1egassion (2,3)

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: d) Let g(x,y) = (3x + y)2(2y + 1) and h(x, y) = 6y2(2x + y) h i) Find дх’ ду’ дх’ ду

A: The given functions are  and

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Q: Show that Sa fdx + gdy = Sa - (16x*y²dx + 8yxʻdy) is independent of path: (10,5) –2) (10,5) ,-2) 4…

A: We are given a line integral as follows : ∫1, -210, 5 fdx+gdy=∫1, -210, 5 -(16x3y2dx+8yx4dy)   First…

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Q: Suppose the solution set of x1 + x2+2x4 What are the equations of the plane at (1,2,3,4) which is…

A: First we find direction vectors of the plane of solutions.

Q: 19. (1) Give the equation of the line going through (3,2, 7) and orthogonal to r+ 2y - 3z = 16 (2) *…

A: 19) 1 Equation of ine through x0,y0,z0 having direction ratios a,b,c is x-x0a=y-y0b=z-z0c

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Q: 5) Find ôw/ôv if w=x² +(y/x), x u-2v+1, and y= 2u +v-2, at the point (u, v) = (0,0)

A: We have to find all partial derivatives first.

Q: 1 (vz,xz,xy) dr where C is the union of the curve y=x* from (0,0,0) to 1+xyz Evaluate (11,0) and the…

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Q: 16. Where does the smallest value f(r, y) + 3ay + y occur on the rectangle (-2, 2) x (-3, 1]? a) It…

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