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

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

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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 +…

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Q: 4) Solve the following linear system or indicate the nonexistence of solution. X1 – 2x2 + 5x3 – 3x4…

A: Or, take x2 = k Hence, solution of the system is x1 = 1+2k, x2 = k, x3 = 1, x4 = 2

Q: 3. Prove that ox + 6x -4X12 is irreducible over Q.

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

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

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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?

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Q: Find the lines curvatures, the first and second fundamental forms of the surface: the surface

A: As per the question we are given a surface. And we have to find its first and second fundamental…

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: / Find the distance from the line x 2 + 1, y 1 +1, z = -(1/2) - (1/2)t to the plane x + 2y + 6z 10.

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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: / (2² + y²) do, where S is the portion of the sphere r? + y? + z² = 9 in the first octant that is…

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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.