Evaluate |/ V1+ x² + y°dS, where S is the helicoid with vector equation r(u, v) = < u cos v, u sin v, v > 0 < u < 4, 0 < v < 2n

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A: To find the gradient of  f(x,y,z)=9x⁵+7y³+6z²

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A: We have to find vector function that represents the curve of intersection of the paraboloid z =…

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…

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Q: The vector equation for the curve of intersection of the surfaces a = y? and z = y in terms of the…

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Q: .3 Evaluate || F · dS, where F = and S is the helicoid with vector equation r(u, v) = 0<u < 1, 0 <…

A: Consider the provided question, Hello. Since your question has multiple parts, we will solve first…

Q: Find a vector of magnitude 2 parallel to the line of intersection of the planes x + 2y + z - 1 = 0…

A: Find a vector of magnitude 2 parallel to the line of intersection of the planes x + 2y + z - 1 = 0…

Q: Q3. Find out values of a, b, c for which curl of vector V is zero, where V = (2xy+ 3 yz) i +(x² +…

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A: Given that, the paraboloid is z=x2+y2 and the cylinder is x2+y2=22. The projection of the of the…

Q: a) Let i = xî + yj + zk, r = |7| and å is a constant vector. Find the value of %3D dxr div

A: We will find out the required value.

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Q: Find a vector function that represents the curve of intersection of two surfaces: z = x² - y? and x²…

A: Idea  1) Solve the equation in term of only one variable (2) assume in term of parametric function…

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A: The Directional Derivative: Let the function f(x, y) be the height of a mountain range at each point…

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Q: if A=i+j+X, B=zi-j+3ksfind vector normal to B and in plane of A and B- ans. $2(3i+9j+x)

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Q: determine where the given vector-valued functions are continuous. V(1) = (Vi-I ,,1 ). V(t): t-1

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A: As per our guidelines we are supposed to answer only first three subparts of question at a time.…

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Q: 1 u (-y°i +x rmal vector to

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Q: f f(x, y, z) = xy: on of vectorî - %3D

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Q: Thẻ nòrmal vector to the plane 3x + 4y – 5z – 6 = 0 is A 3i+ 4j – Sk B 3i + 4j + Sk C 3i+ 4j – 6k D…

A: It is normal vector form.

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A: Given: 3z3+x2y-y2x=1 at P(1,-1,1)

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Q: Two plane curves are defined by the vector functions r1 (t) = (t, 2t – 4) and r2 (u) = (2u, u²).…

A: r1t=t,2t-4 and r2u=2u,u2 For the intersection point, t=2u   ...1u=t22t-4=u2    ...2 Convert the…

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A: Since the vector is contained in the plane, so all the points of the line intersect with the plane.…

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A: Given equations are x2+y2+4z2=4 ..... (1) and x2+z2=1 ..... (2) From equation (1) z2=(4-x2-y2)/4…

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Q: Find a vector equation with parameter t for the line of intersection of the planes x + y + z = 4 and…

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A: Since you have asked multiple questions in a single request, we would be answering only the first…

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A: We apply the cross product to find the given function and simplification needed.

Q: Find a vector equation for the curve of intersection of the surfaces x^2 + y^2 = 4 and z = xy.

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Q: The spherical equivalent of the vector B = yi + (x + z)j located at (-2,6,3) is given by

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Q: Find a vector tangent to the curve of intersection of the two cyclinders a2 + y? = 8 and y² + 22 = 8…

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Q: Find the Duf of f(x, y,z) = z In(x+ y) + e3y on the vector u = 3i -j-4k at Po(1,0,1)

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Q: Which of the following vector functions represents the curve of intersection of the cylinder x2 + z2…

A: We have to find vector functions representing curve of intersection of cylinder and plane. Plane…

Q: Suppose a vector function F(x, y) = 3xi + 2xyj + y ln zk moves along a path C where x = t2, y = t +…

A: The formula to find the work done by the vector function helps to find the required work done. The…

Q: Let F(x, y, z) = 5x² + 2y2 + 522. For which unit vector 0 will the directional derivative DoF at (2,…

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

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Q: Find a vector function that parameterizes the curve of intersection between the surfaces y^2-z^2=x-2…

A: To determine the vector function for the curve of intersection between the surfaces.