Use Stokes' Theorem to evaluate F. dr. F(x, y, z) = 8(x – y)i+8(y – 2)j+8(z – x)k where C is the circle x² + y² = a² in the xy-plane with a counterclockwise orientation looking down the positive z-axis. NOTE: Enter the exact answer in terms of a. F· dr

Q: a) f : R? → R, f (x, y) = Vy sin x 5) f : R2 → R. f (r. u) = GGrul + In (a2 + 1? – 1). /4 – 72 -

A: We will find the domain

Q: c) Use Stokes' theorem to evaluate F. dr where F = z' i+yJ + xk and C is the triangle with vertices…

A: Stokes theorem is used to find the line integral of the vector point function

Q: 5. Find u-dr for a unit square in the first quadrant with vertex at the origin by Stokes's C theorem…

A:

Q: Let L1 be the line through the points P(1,0,2) and Q(2,1, 1), and L2 be the line defined by the…

A: Given- Let L1 be the line through the points P1, 0, 2 and Q2, 1, 1, and L2 be the line defined by…

Q: if u and v are orthogonal, than u,v =(0,0,0) b. u x v is a scalar c. v.v = ||v|| d. if π/3 is the…

A: If u and v are orthogonal then u.v=(0,0,0) a true

Q: Find the equation for the tangent plane to the surface x-9xyz +y= - 11z at the point (-1,-1,-1). O…

A: The given surface is x2-9xyz+y2=-11z2 and the point is -1,-1,-1.

Q: nd the tangent plane to the equation z = a? – 4y? – 2y at the point ( – 3, 3, – 33)

A: In this question, concept of tangent  is used. Tangent A tangent is the line that runs parallel to…

Q: (b) Calculate the distance from the point P(3,–1, 2) to the plane with equation 2x – y +z = 4.

A:

Q: Let ♬ =. Use Stokes' Theorem to evaluate So F. dr, where C is the curve of intersection of the…

A:

Q: Let R = (c, 1,-1) where c denotes a real number. Let ä denote the plane x + y – z = 2. Find the…

A: Given Information -  The distance from the point R = (c,1,-1) to the plane x+y-z = 2 is 2. We have…

Q: Use Stokes' Theorem to evaluate curlF · dS, where

A: Let, F→=xyz , xy , x2yz. Stokes theorem states that ," Where C is the boundary of surface oriented…

Q: Let F = . [F Use Stokes' Theorem to evaluate F.dr, where C is the triangle with vertices (7,0,0),…

A: Given,             F→=4x+y2, 8y+z2, 9z+x2, Use Stokes' Theorem to find:                ∫CF→·dr→,…

Q: Given F = (yz,x+y+=,xz), determine curl F .

A: Curl F ( -1, y-z ,1-z)

Q: Let F = . Use Stokes' Theorem to evaluate F. dr, where C is the triangle with vertices (7,0,0),…

A: Given that, F→=5x+y2, 2y+z2, 8z+x2 And vertices of the triangle are, 7,0,0, 0,7,0, 0,0,7. To find…

Q: Find the point on the graph of z = - (2x² + y²) at which vector n = P = (-12, -10, -1) is normal to…

A: To find the point P on the graph of z=-2x2+y2 at which vector n=-12, -10, -1 is normal to the…

Q: Given a point (0, 30, 0) for which z + y ≤ 1, note that the point To, yo, 1 √1-x² - y2 is on the…

A: Given that:

Q: Which of the following are parametric equations of the line of intersection of the planes x+2 z=3,…

A: We have to check

Q: R] [CLO 8] Give an example of a point in Quadrant III of the rtesian plane.

A: we will find the required.