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Math Help - equation of plane tangent

  1. #1
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    equation of plane tangent

    Let S be the surface parameterised by
    r(u,v):=(e^ucosv,u,e^usinv), <br />
u\in\Re, v\in[0,2\pi]
    (i) Find the equation of the plane tangent to S at r(u,v).
    (ii) At what points is the tangent plane to S parallel to the x-y plane?
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  2. #2
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    Quote Originally Posted by maximus101 View Post
    Let S be the surface parameterised by
    r(u,v):=(e^ucosv,u,e^usinv), <br />
u\in\Re, v\in[0,2\pi]
    (i) Find the equation of the plane tangent to S at r(u,v).
    (ii) At what points is the tangent plane to S parallel to the x-y plane?
    r_u= (e^ucos(v), 1, e^usin(v)) and r_v= (-e^usin(v), 0, e^ucos(v)) are two vectors in the tangent plane. Their cross product will be perpendicular to the plane. The tangent plane will be parallel to the xy-plane when that normal vector is in the z direction (has both x and y components equal to 0).
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