(d) Use Stokes' theorem to evaluate f. F.dr where F = z?î + y²j + xk and C is the triangle with vertices (1, 0, 0), (0, 1, 0), and (0, 0, 1). The unit vector normal is upward.

Q: Find a unit normal vector of the surface at the given point P. x² + y² = 25, P: (4, 3,6)

A: The equation is x2+y2=25 and the point is P4, 3, 6. Now, the unit normal vector is n^=∇ϕ∇ϕ. Now, for…

Q: Find the cartesian equation of the plane that is normal to the vector n = -3i – 4j+4k and includes…

A: n=-3i-4j+4k  and P(2,-7,5)

Q: express vector in spherical components.

A: According to the given information, it is required to express the following in spherical components.…

Q: Evaluate /| F. d5 , where F = and S is the helicoid with - vector equation r(u, v) = 0 < u < 1, 0…

A: To evaluate the below vector surface integral. ∫∫SF⋅dS