Answer
$\frac{3}{\sqrt 2}$ or,
$\frac{3\sqrt 2}{2} $
or $\approx 2.12$
Work Step by Step
$1(1+t)-1(2-t)+2(-1+2t)=0$
$0=1+t-2+t-2+4t$
$6t-3=0$
$t= \frac{1}{2}$
Point on the line closet to the origin is:
$(1+1/2,2-1/2,-1+2(1/2))=(3/2,3/2,0)$
Distance$=\sqrt {(3/2-0)^2+(3/2-0)^2+(0-0)^2}$
$=\sqrt \frac{9}{2}$
$=\frac{3}{\sqrt 2}$
$=\frac{3\sqrt 2}{2} \approx 2.12$
Answers are:
$\frac{3}{\sqrt 2}$ or,
$\frac{3\sqrt 2}{2} $
or $\approx 2.12$