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(a) Draw and parametrize the circle of radius two centered at (1,-1,1) and lying on the plane z+y+z=1. Hint: find two orthogonal unit vectors

(a) Draw and parametrize the circle of radius two centered at (1,-1,1) and lying on the plane z+y+z=1. Hint: find two orthogonal unit vectors which are parallel to the plane. (b) Find parametric equations for two circles C and C in space such that C and C have the same radius: . C and C intersect at the points P(2,-1,3) and Q(2, 1, 3) and nowhere else.

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