Question 5
For two vectors $\mathbf{a}$ and $\mathbf{b}$ in the Cartesian space, it is known that $$|\mathbf{a}+\lambda\mathbf{b}|\ge|\mathbf{a}|$$ for all real numbers $\lambda$. Find the largest possible value of the scalar product $\mathbf{a}\cdot\mathbf{b}$.
(Note: If you think that the set of all possible values is unbounded, enter 9999.)
(Note: If you think that the set of all possible values is unbounded, enter 9999.)