Verifying Stokes’ Theorem Verify that the line integral and the surface integral of Stokes’ Theorem are equal for the following vector fields, surfaces S. and closed curves C. Assume that C has counterclockwise orientation and S has a consistent orientation. 9. F = 〈 y – z , z – x , x – y 〉; S is the cap of the sphere x 2 + y 2 + z 2 = 16 above the plane z = 7 and C is the boundary of S.
Verifying Stokes’ Theorem Verify that the line integral and the surface integral of Stokes’ Theorem are equal for the following vector fields, surfaces S. and closed curves C. Assume that C has counterclockwise orientation and S has a consistent orientation. 9. F = 〈 y – z , z – x , x – y 〉; S is the cap of the sphere x 2 + y 2 + z 2 = 16 above the plane z = 7 and C is the boundary of S.
Verifying Stokes’ TheoremVerify that the line integral and the surface integral of Stokes’ Theorem are equal for the following vector fields, surfaces S. and closed curves C. Assume that C has counterclockwise orientation and S has a consistent orientation.
9.F = 〈y – z, z – x, x – y〉; S is the cap of the sphere x2 + y2 + z2 = 16 above the plane
z
=
7
and C is the boundary of S.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Identify the surface by eliminating the parameters from the vector-valued function
r(u,v) = 3 cosv cosui + 3 cosv sinuj + Śsinvk
a. plane
b. sphere
c. paraboloid
d. cylinder
e. ellipsoid
d
b
a
e
(D
Please show all work!
Vector F is mathematically defined as F = M x N, where M = p 2p² cos + 2p2 sind while N
is a vector normal to the surface S. Determine F as well as the area of the plane perpendicular
to F if surface S = 2xy + 3z.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
01 - What Is an Integral in Calculus? Learn Calculus Integration and how to Solve Integrals.; Author: Math and Science;https://www.youtube.com/watch?v=BHRWArTFgTs;License: Standard YouTube License, CC-BY