 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2023/paper-2/11/c/i/solution

P_{1}

, since coplanarity of points concerns an affine plane that need not contain the origin. The three displacement vectors are

u = (0, 1, 1)^{T}, v = (1, 2, 1)^{T}, w = (2, 3, 2)^{T} .

u \times v = (- 1, 1, - 1)^{T}

and its dot product with

w

- 1

. Since the scalar triple product is nonzero,

The four points do not lie in a common plane.

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