 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2006/paper-1/5/e/solution

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

Put

S = a^{- 2} + b^{- 2} + c^{- 2}

d = n / S

. Comparing its coordinates with

(λa, μ b, ν c)

gives

λ = \frac{a ^{- 2}}{S}, μ = \frac{b ^{- 2}}{S}, ν = \frac{c ^{- 2}}{S} .

Their sum is one, as the plane equation requires.

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