For R(u,v)=2cos U I + v J+ 2sin U K, Find The...

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For r(u,v)=2cos u i + v j+ 2sin u k, find the rectangularequation for the surface by elimnating the parameters from thevector valued function. Identify the surface and sketch itsgraph.

 

Answer No.1

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R(u,v)=2cos u i + v j+ 2sin u k = xi+yj+zk r2=x2+y2+z2=4cos2+v2+4sin2u+v2=4+y2 i.e.x2+z2=4 this the equation of acylinder with the radius 2 and y-axis as its axis.

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