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

Find parametric equations for the lines in The line through the origin parallel to the vector $2j+k$
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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 $p0=\left({x}_{0},{y}_{0},{z}_{0}\right)$ and parallel to the vector is $v=\left(ai+bj+ck\right)$
$x={x}_{0}+at,y={y}_{0}+bt,z={z}_{0}+ct$

Step 2 To find parametric equations for the lines Here

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 $x=0,y=2tandz=t$ .