 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2003/paper-1/1/c/solution

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

Suppose

r A + s B + t C = 0

. Take its dot product successively with

a, b, c

. The reciprocal pairings give

r = s = t = 0

. Thus

A, B, C

are linearly independent and therefore noncoplanar in three dimensions.

 New to topics? Read the docs here!