The surface parametrized by r(u, v)=(5 cos u sin v, 5 sin u sin v, 5 cos v) is a
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The surface parametrized by r(u, v)=(5 cos u sin v, 5 sin u sin v, 5 cos v) is a
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- Which lines or line segments or rays must be drawn or constructed in a triangle to locate its a orthocenter? b centroid?what is equation geodesics on a circular cylinder parametrized by f(u, v)=(cos u, sin u, v) are straight lines, circles, and helices.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= TT IN 2
- The path r(t)=(5 sin t) i+(5 cos t) j describes motion on the circle x^2+y^2=25. Find the particle's velocity and acceleration vectors at t=π/3 and π/6, and sketch them as vectors on the curve.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 FalseThe 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?
- 2 Sketch the parametric surface x = Vu“ +v , y = u, z = v. luFind the distance from the point (3, 2, 5)to the line with parametric equations x=t,y =l +t ,z = 2 + t.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 2
- The vector equation r (u, v) = u cos vi + u sin vj + vk, 0 < v < 5x, 0 < u < 1, describes a helicoid (spiral ramp). What is the surface area? 10.25piFind an equation of the normal line to the parametric surface given by R(u, v) = ((2+ cos v) cos Tu, U +(1 – u) sin v, (1+ cos v) sin Tu) at the point where (u, υ) (1, π).Consider the surface S parametrized by R(u, v) = (uv, sin u, cos v). Find an equation for the tangent plane to S at the point (, 1, ).