4. Obtain the equation of the tangent plane to the surface with parametric representation r(u, v) = u²i + 2u sin vj + u cos v k %3D at (1,0, 1).
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A: This question is related to three dimensions geometry.
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A: we have to following integral
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Q: 12. Find the area of the surface generated when the curve y =+,on [1,2] is rotated about the x-axis.
A: solution is given below...
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Q: 2. Find the area of the surface obtained by rotating the curve: y = Vx +1,1<x<5 about the Х-ахis
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- The two surfaces x2 + y2 + z2 = 6 and 2x2 + 3y2 + z2 = 9 intersect at the point(1,1,2). Find the angle between the tangent planes at the point(1,1,2). Also, find the tangent vector to the curve in which surface intersect?Find an equation of the tangent plane (in the variables x, y and z) to the parametric surface.r(u,v)=⟨4u,4u^2+5v,−3v^2⟩ at the point (4,-6,−12).Equation of the tangent plane to the surface 7 (u,v) at (uo,Vo) is given by 7-7(uo, Vo)× Ñ(uo,Vo)=0. Select one: O True O False
- Find the equation of tangent plane to the surface x? + 2y? + 3z? = 21 which is parallel to the plane 2x + 4y + 6z = 3.Find the equation of the tangent plane to the surface 2= 4 + 3y + 7zy at the point (0,-1, 3).Let r(t) = cost i + e^t j + t^2 k be given. A) Find the unit tangent vector to the curve at any point. B) Write the parametric equation of the tangent line to the curve at (1,1,0).
- Find an equation of the tangent plane to the parametric surface R(u, v) = ((u - sin u) cos v, (1 - cos u) sin v, u) at the point where u = v= FIN 2Find an equation for the plane tangent to the level surface x² + y? +z = 4 at the point Po(1,1, 2). Then find the parametric equations for the line that is normal to the surface at Po.Find the equation = 3x² + 4y² + 9xy at the point (2, 0, 12). 2 = of the tangent plane to the surface
- Find equations of the Normal plane and Osculating plane of the y = 2t, curve x = 2 sin 3t , z = -2cos 3t at the point (0 , n,-2).5) Find the equation of the tangent plane to the surface exyz = x + 2y + 3z at the point (3,-1,0).Find the angle of inclination 8 = x² + y² = 17, (4, 1, 5) Submit Answer of the tangent plane to the surface at the given point. 0