7-14 Use Stokes' Theorem to evaluate Sc F. dr. In each case C is oriented counterclockwise as viewed from above, unless otherwise stated. 14. F(x, y, z) = (x³ - z, xy, y + z²), C is the curve of intersec- tion of the paraboloid z = x² + y² and the plane z = x X4 N ZA Z=x^ z = x² + y²

Q: Find parametric equations for the line through the point P(3, 6, 4) that is parallel to the plane x…

A:

Q: Find a parametrization of the line in which the planes x- 2y - 2z = 3 and -3x + 3y + 3z = -6…

A:

Q: Your friends correctly calculate the gradient vector for f(x, y)=x²+y at the point (2,-3) as…

A:

Q: Match each parametrization with the corresponding surface. (i) (ii) (iii) (iv) (v) Answer Bank (u,…

A:

Q: 3. Find a vector function that represents the curve of intersection of the paraboloid z =. and the…

A: To find the vector function that represents the curve of intersection of the paraboloid z=x2+y2, and…

Q: 4. Consider the vector function r(z, y) = (x, y, x² + 2y*). (a) Re-write this vector function as…

A: For the given vector function, PART A The surface function is given by, f(x,y)=xi^+yj^+(x2+2y2)k^…

Q: TRUE OR FALSE. A plane curve C defined by the parametric equations x = f(t) and y = g(t), where t is…

A: check the given statement is true or not.

Q: Assume that the cylinder in Figure has equation x² + y² = r² and the plane has equation z = ax + by.…

A: To find the vector parametrization r(t) of the curve of intersection using the trigonometric…

Q: 12. Let C represent the curve of intersection between the cylinder x² + y² = 4 and the plane z = 10…

A: The plane z=10-x will cut the cylinder x2+y2=4 to give an ellipse.

Q: Let F(x, y, z)= xyi+yzj+k and a smooth curve C given by the line segment from Answer format: a, b, c…

A:

Q: The equation for a plane tangent to z = f(x, y) at a point (xo, Yo) is given by z = f(xo, Yo) +…

A:

Q: Find the distance between the skew lines with parametric equations x = 3 + t, y = 1 + 6t, z = 2t,…

A: I am attaching image so that you understand each and every step.

Q: Consider the paraboloid given by the equation: z = x^2 + y^2 Find the equation of the tangent…

A: at point (1, 2, 5)at point (1, 2, 5)

Q: Find both parametric and rectangular representations for the plane tangent to r(u, v) = u’i + u…

A: Answer is mentioned below

Q: 8. A line initiated from (1,0,2) and parallel to a vector i+j+k what is the parametric equation of…

A: we have to find equation of line in 8.

Q: This surface (dreamed up by Steiner while in Rome) looks smooth but is non-orientable, with the…

A: Given: The parametrization for the surface is given by σ(u,v)=x,y,z=sin2usinv,sin2ucosv,cos2usin2v…