Solution
= Solution
The <triangle inequality> for the two <unit vectors> gives $0<\|u+v\|\le2$. Taking reciprocals and using the negative sign in $\lambda=-1/\|u+v\|$ yields
$$
\boxed{\lambda\le-\frac12.}
$$
In fact equality would require $u=v$, by the equality condition in the <Cauchy-Schwarz inequality>. Since the two vectors here are <linearly independent>, the inequality is strict for every admissible pair.