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 \(a = 0 , b = 2 , c = 1 , x_0 = 0 ,y_0 = 0 and z_0 = 0\) 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 \(x = 0 , y = 2t and z = t\) .

\(x = x_0 + at , y = y_0 + bt , z = z_0 + ct\) Step 2 To find parametric equations for the lines Here \(a = 0 , b = 2 , c = 1 , x_0 = 0 ,y_0 = 0 and z_0 = 0\) 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 \(x = 0 , y = 2t and z = t\) .