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

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

2021-02-13
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 $$x = 0 , y = 2t and z = t$$ .

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