Evaluate F. dS, where F = < y, – x, z² > and S is the helicoid with vector equation r(u, v) < u cos v, u sin v, v > , 0 < u < 3, 0 < v < 27 with upward orientation. ||

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

A: since, y,-x,z3 and, ru,v=u cosv, u sinv,v So, F⇀ru,v=u cosv,-u sinv, v3 Now the normal upward vector…

Q: [15] (2) Consider the function f: R² → R, f(x, y) = x² − 2xy + 2y² Determine Vf. a) b) c) d) GIVEN:…

A: Sine you have posted a question with multiple subparts we will solve first three subparts for you.…

Q: (a) F(t)=(2 sint)i + (2 cost)j from the point A(2, 0) to the point B(-2, 0)

A: To find the arc length of given function

Q: Find an expression for a unit vector normal, no, to the surface x = (4 – cos (v)) cos (u), y = (4 –…

A: The complete solutions are given below

Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

A: The objective is to find the directional derivative of the given function h(r,s,t) along the point…

Q: Find the directional derivative of the function at the given point in the direction of the vector…

A: This is a problem of Vector Calculus.

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.