Given, points $A(1,2,-1)$ and $B(-1,0,1)$ and $P$ divides the line segment externally in the ratio
$1: 2$
For external division, coordinates are
$\left[\frac{m_1 x_2-m_2 x_1}{m_1-m_2}, \frac{m_1 y_2-m_2 y_1}{m_1-m_2}, \frac{m_1 z_2-m_2 z_1}{m_1-m_2}\right]$
$\begin{aligned} & =\left[\frac{1(-1)-2(1)}{1-2}, \frac{1(0)-2(2)}{1-2}, \frac{1(1)-2(-1)}{1-2}\right] \\ & =\left[\frac{-1-2}{-1}, \frac{-4}{-1}, \frac{3}{-1}\right] \\ & =[3,4,-3]\end{aligned}$
So, $P Q=\sqrt{(3-1)^2+(4-3)^2+(-3+1)^2}$
$\begin{aligned} & =\sqrt{(2)^2+(1)^2+(-2)^2} \\ & =\sqrt{4+1+4}=3 \text { units }\end{aligned}$