a) Setting , show that the three projection equations for the three lines in Equation 5 can be written as where for . (b) Show that the three pairs of equations in part (a) can be combined to produce where . [Note: Using this pair of equations, we can perform one complete cycle of three orthogonal projections in a single step.] (c) Because tends to the limit point as , the equations in part (b) become as . Solve this linear system for . [Note: The simplifications of the ART formulas described in this exercise are impractical for the large linear systems that arise in realistic computed tomography problems.]

Fall 2011 MA 16200 Study Guide - Exam # 1 ▯ (1) Distance formula D = (x2− x 1 + (y −2y ) 1 (z − 2 ) ;1equation of a sphere with cen- 2 2 2 2 ter (h,k,l) and radius r: (x − h) + (y − k) + (z − l) = r . −→ (2) Vectors in R and R ; displacement...