Find parametric equations for the lines in The line through the origin parallel to the vector 2j + k

Step 1 Given The vector equation is $0i+2j+k$ The line passing through origin , origin is ( 0 ,0 ,0) The parametric equations for the line passing through the point $p0=(x_0,y_0,z_0)$ and parallel to the vector is $v=(ai+bj+ck)$
$x=x_0+at,y=y_0+bt,z=z_0+ct$

Step 2 To find parametric equations for the lines Here $a=0,b=2,c=1,x_0=0,y_0=0and{z}_0=0$

Now plug this values in parametric equation $x=0+0t,y=0+2t,z=0+1t$
$x=0,y=2t,z=t$

Therefore parametric equations for the line is $x=0,y=2tandz=t$ .