Step 1:

Let $OA$ be the line joining the origin (0,0,0) and the point $A(2,1,1)$

Let $BC$ be the line joining the points $B(3,5,-1)$ and $(4,3,-1)$

The direction ratios of $OA$ are (2,1,1) and $BC$ are [(4-3),(3-5),(-1+1)]

(i.e)(1,-2,0)

Step 2:

It is given $OA$ is perpendicular to $BC$

Hence $a_1a_2+b_1b_2+c_1c_2=0$

Substituting for $(a_1,b_1,c_1)$ and $(a_2,b_2,c_2)$ we get

$2\times 1+1\times -2+1\times 0$

$\Rightarrow 2-2+0$

$\Rightarrow 0$

Hence $OA$ is $\perp$ $BC.$