 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2025/paper-1/11/b/iv/solution

\hat{n}

. Since the plane passes through the origin, the distance is

d = ∣ p \cdot \hat{n} ∣ = \frac{∣2 + 0∣}{2} = 2 .

For a direct check, the closest point on a plane is

p - (p \cdot \hat{n}) \hat{n} = (1, 2, - 1)^{T}

, whose displacement from

p

2

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