The vector equation r (u, v) = u cos vi + u sin vj + vk, 0 < v < 5n, 0 < u < 1, describes a helicoid (spiral ramp). What is the surface area? 10.25pi

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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: .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…

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Q: The vector equation r(u,v)=ucosvi+usinvj+vk, 0≤v≤4π, 0≤u≤1, describes a helicoid (spiral ramp). What…

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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: 1. Find the unit normal vector to the surface z = Vx2 + y? at the point (3, 4, 5).

A: A detailed solution is given below

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Q: Evaluate F· dS , where F = and S is the helicoid with vector equation r(u, v) upward orientation.…

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Q: Find the area of the helicoid (or spiral ramp) with vector equation r(u, v) = ucos(v) i + usin(v) j…

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Q: R(u, v) = (uv, u sin v, v cos u)

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Q: Use cylindrical coordinates. Evaluate z dv, where E is enclosed by the paraboloid z = x2 + y2 and…

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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: Evaluate F. dS, where F = and S is the helicoid with vector equation r(u, v) = 0< u < 2, 0 < v <…

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