 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/f/solution

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

a

is orthogonal to both

b

and

c

, so

a \cdot (b - c) = 0

. Also

d \cdot b = d \cdot c = 1/ S

, hence

d \cdot (b - c) = 0

(a - d) \cdot (b - c) = 0

. Both vectors are nonzero, so

the angle is π /2.

 New to topics? Read the docs here!