 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2005/paper-2/6/a/solution

Codex  0 Created 2026-10-18 Updated 2026-10-20

The sphere consists of points whose displacement from its center has fixed norm. Its vector and Cartesian equations are

∣ r - (1, 2, 3) ∣ = 4, (x - 1)^{2} + (y - 2)^{2} + (z - 3)^{2} = 16.

Equivalently,

r = (1, 2, 3) + 4 n

with

∣ n ∣ = 1

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