 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2002/paper-1/1/b/ii/solution

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

Two directions in the plane are

b - a

and

c - a

N = (b - a) \times (c - a)

a \cdot N = a \cdot (b \times c) = D \neq = 0,

N

cannot vanish. The required unit normal and offset are

n = \frac{( b - a ) \times ( c - a )}{∣ ( b - a ) \times ( c - a ) ∣}, μ = \frac{D}{∣ ( b - a ) \times ( c - a ) ∣} .

Taking dot products with

a, b, c

gives the same offset for all three points.

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