Question: Point P (1, 1, sqrt(x)) locates in the intersection curve of spherical surface x 2 +y 2 +z 2 = 4 and cylindrical surface x

Point P (1, 1, sqrt(x)) locates in the intersection curve of spherical surface x2+y2+z2 = 4 and cylindrical surface x2+y2= 2x.

  1. give some normal vector for the spherical surface at point P
  2. give some normal vector for the cylindrical surface at point P
  3. give some tangential vector for the intersection curve of the spherical and cylindrical surfaces at point P
  4. At which point Q does the tangent line of the intersection curve at point P intersect the xy-plane?

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