If a parametric surface given by r₁(u, v) = f(u, v)i + g(u, v)j + h(u, v)k and −4

Q: Does the Divergence Theorem apply to surfaces that are not closed?

A: By Stokes' theorem:

Q: 10. Find the coordinates of the point of intersection of the line L: x = -1+ 3t, y = 2 – 2t, z = 3 +…

A:

Q: find the angles between the curves v=u2, v=u3, lying on the surface  x=u2+v2 y=u2-v2 z=uv+3u+2v

A: As per the question we are given the parametric form of a surface in 3d as : x = u2 +v2 y = u2 - v2…

Q: 3. Let C be the circle x + y = 16 and let S be any surface above the xy-plane with C as its…

A:

Q: What is the tangent plane equation of sphere f(x, y. :)=x² + y² += =6 at point (1,-1,2)? O a.…

A: I hope that this solution will help you .Thankyou. Best regards.

Q: 8.) Find the planes tangent to the following surfaces indicated points: a:) x² + 2y ²2/3 X ² = 10₁…

A:

Q: 2) Draw contour maps for functions f(x, y) = x² - 4y², and g(x, y) = x² + 4y². What shape. are these…

A: The contour of function f(x,y) represents parabolas.

Q: Find the angle between the surfaces x² + y² + z² = 41 and z = x² + y²-11 at the point (4, 0, 5):

A:

Q: f) Every continuous map T² RP2 is homotopic to the constant map.

A:

Q: What is the total length of the curve of intersection of the surfaces x2 + y2 + z2 = 4 and y2 + 2z2…

A:

Q: calculate ∫Cy(x-z) ds, where C is the intersection of the surfaces x2+y2+z2=9 x+z=3

A:

Q: x-2 z+4 • Let L:*²=+3 = 2²+ and M: 2x - 3y +z = 6 are line and 3 2 5 plane and let P be the…

A: We have to find the equation of line

Q: .Calculate the dstance between tve point (3, -2) and the plane Z Xty-2+1=0.

A: The distance between the point (a, b, c) and the plane Ax+By+Cz+D=0 is given by,

Q: If (x, y) and (X, Y) are the coordinates of the same point referred to two sets of rectangular axes…

A: and are the co-ordinates of the same point referred to the set of rectangular axes with same origin.

Q: Where does the parametric line ( 2 + 2 t , t , t ) intersect the plane x+y-3z=4?

A:

Q: Q3b): Compute zdz over several contours (i) The line from 1 to 1+ i. (ii) The circle of radius 1…

A: let fz=1z.  Since f(z) has an antiderivative in an open region D, then the line integral over given…

Q: Which of the following is the least distance from the point (2, –1,1) to the plane x + y – z = 2?

A: Given: The plane equation is x+y-z=2and the distance from the point is 2,-1,1 To find the least…

Q: 4) Find the families of lines of curvature of the surface z = r + y? .

A: Given: z=x2+y2

Q: Consider the surface S of equation 2 = x² + y*" An equation for the tangent line tangent to S at…

A:

Q: The plane given by x + y + 2z = 0 and the line given by x = 2 + t y = 1 - 2t z = 3 + t

A: The plane given by x + y + 2z = 0 and the line given by x = 2 + t;  y = 1 - 2t ;  z = 3 + t To find…

Q: Suppose the solution set of x1 + x2+2x4 What are the equations of the plane at (1,2,3,4) which is…

A: First we find direction vectors of the plane of solutions.

Q: 19. Find the distance from the point (3, -2,7) to the plane 4x – 6y + z = 5. Show all necessary work…

A: A detailed solution is given below.

Q: 11) A point on the surface 2x + y? + z? = 4 at which the tangent plane is parallel to the plane x -…

A:

Q: Suppose you head toward the xy-plane from the surface x? + y? – 2² = –1 at the point (1, 1, v3) by…

A: given,     x2+y2-z2=-1 at the point 1,1,3

Q: Compute the intersections of the curve xy = 1 and the lines x +y = 5/2, x+y = 2, x+y = 0, x=0 , x=1…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…