Equation of a Sphere: Three-dimensional space

14. Find an equation of the sphere that passes through the origin and whose center is (1, 2, 3).

19. (a) Prove that the midpoint of the line segment from P1(x1, y1, z1) to P2(x2, y2, z2) is

(((x1 + x2)/2), ((y1 + y2)/2), ((z1 + z2)/2))

(b) Find the lengths of the medians of the triangle with vertices A(1, 2, 3), B(-2, 0, 5), and C(4, 1, 5).

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