10. Let two non-zero and non-collinear vectors $a, b$ in the same plane satisfy $b \perp (a-b)$. Then for any $x \in \mathbf{R}$, the range of $|a-b x|$ is $\qquad$ (expressed in terms of vectors $a, b$).
10. $[|a-b|,+\infty)$.

Let $\overrightarrow{O A}=a, \overrightarrow{O B}=b, b x$ represent any vector collinear with $\overrightarrow{O B}$, $|a-b x|$ represents the distance from point $A$ to any point on line $O B$, and $|\boldsymbol{a}-\boldsymbol{b}|$ represents the distance from point $A$ to $B$.
When $b \perp(a-b)$, $A B \perp O B$.
By the property that the perpendicular distance from a point to a line is the shortest, for any $x \in \mathbf{R}$, we have $|a-b x| \geqslant|a-b|$.