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- Consider the spherical surface E with center at C= ( 4, 3, 2 ) and radius 4 . Let π be the tangent plane to E at the pointP=C+ 4u,where u is the reverse of the vector v = ( 4, 3, 4 ).If the general equation of π is given byπ:ax+y+cz=d, so the value of d is:Find the distance between the skew lines with the given parametric equations. x = 2 + t, y = 3 + 6t, z = 2tx = 1 + 2s, y = 5 + 14s, z = -3 + 5s.Consider the paraboloid given by the equation: z = x^2 + y^2 Find the equation of the tangent plane to the paraboloid at the point P(1,2,5) .
- Can you help me with question 2 in the picture? It involves finding the points where a tangent plane to a surface is parallel to another plane.Find an equation of the tangent plane to the given parametric surface at the specified point. x = u + v, y = 3u^2, z = u - v; (2,3,0)1. (Section 17.7) Use Stokes’ Theorem to calculate the work done by −→F (x, y, z) = ex2ˆı − 2xzˆj + xˆk in moving a particle aroundthe closed path determined by the intersection of positively oriented surface S : x + 4y + 2z = 4 and the coordinate planes.
- please show and explain how I would be able to find the equation of the plane perpendicular to the curve: r(t) = <t sin t, 3t, 2t cos t> = at t = π/2 (not graded)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).Show that the parametric equations x a cosh u cos v, y b cosh u sin v c sinh u represent a hyperboloid of one sheet
- Convert the following quadric surface into spherical coordinates. (x-3)^2+y^2+(z+1)^2 = 1Find the distance between the skew lines with parametric equations x = 1 + t, y = 3 + 6t, z = 2t, and x = 2 + 2s, y = 6 + 14s, z = −3 + 5s.Consider the parametrization r (u, v) = (v, 2 cos u, 4 sin u), with u ∈ [ 0 , π/2]and v ∈ [1, 3], which describes the surface S represented in the following graph: image1 A normal vector to the surface S, with the orientation given in the previous graph, corresponds to: image 2