Solution
= Solution
Parametrize the line by $\mathbf r(t)=(t,t,t)$, $0\leq t\leq1$. Its <tangent vector> is $(1,1,1)$. On this line the three <force> components sum to $\mu t+(1-\lambda)t+(\lambda-1-\mu)t=0$. Therefore the <line integral> is $\boxed{\int\mathbf F\cdot d\mathbf r=0}$ for every parameter choice.