 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2003/paper-1/7/i/solution

Parametrize the line by

r (t) = (t, t, t)

0 \leq t \leq 1

(1, 1, 1)

. On this line the three force components sum to

μ t + (1 - λ) t + (λ - 1 - μ) t = 0

. Therefore the line integral is

\int F \cdot d r = 0

 New to topics? Read the docs here!