This homework set focuses on concepts applied in Nuclear Magnetic Resonance (NMR) and Magnetic Resonance Imaging (MRI) scanners used used in medical imaging machines [3], as well as similar concepts used in scientific and industrial imaging machines [1. Definition 1 The Radon Transform [RF](P) of a function f : R3 → Rover the surface of a plane P in space R3 is the surface integral [4, § 15.7] of f over the plane P [RS](P) = M. FaA. A plane Pp, n may be specified by a unit normal vector n perpendicular to P and the distance p from the origin 0 to the plane Pp, n in the direction n. A Cartesian equation for the plane Pp, n may then use a dot product with n. Such integrals arise as measurements in medical diagnostic imaging devices known as Nuclear Magnetic Reso- nance (NMR) or Magnetic Resonance Imaging (MRI) [2], [3]. For this problem, the function f has a constant value c > 0 everywhere inside the ball B with radius R > 0 centered at the origin 0, and f has the constant value () everywhere outside the ball B. Find (Rf](Pp, n): f(x, y, z) = { C, 0, x2 + y2 + x2 < R?; RP < x2 + y2 + 22The plane Pp, n = is at a distance p from the origin 0 and perpendicular to the unit normal n (a, b, c), so that a² + b2 + c2 = 1. Finding (Rf](Pp, n) means finding the surface integral of f over the plane Pp, n. The result may depend on c, p, and n. Sketching a picture with the plane and the domain of the function may help.