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  3. 1.2 a large circle on a sphere is a circle that fo

1.2 A large circle on a sphere is a circle that forms the intersection of the sphere...

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Basic Math

1.2

A large circle on a sphere is a circle that forms theintersection of the sphere with a plane through the center of thesphere. Consider the large circle C that arises the intersectionsphere x2 + y2 + z2 = 1 and theplane x + y + z = 0.

(a) Express the equations of the specified large circle C usingspherical coordinates.

(b) Express the equations of the large circle C usingcylindrical coordinates.

(c) Determine a parameterization of C by writing

r (t) = u cos t + v sin t,

where u and v are two orthogonal unit vectors in the plane thatcut out C.

(d) Determine the speed and velocity of a particle travelingalong the large circle

according to the parameterization in part (c), when theparameter refers to the time.

Answer & Explanation Solved by verified expert
4.1 Ratings (553 Votes)
Consider the sphere 1Also consider the plane 2aThe objective is to find the largecircle which is the    See Answer
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