## Thomas' Calculus 13th Edition

$x=0,y=0, z=t$
We know that the parametric equations of a straight line for a vector $v=v_1i+v_2j+v_3k$ passing through the point $P(a,b,c)$ are given by $x=a+t v_1,y=b+t v_2; z=c+t v_3$ We have, $P=(0,0,0)$. The point P lies on the z-axis, which means that we have the vector $v=\lt 0,0,1 \gt$ Our parametric equations are: $x=0+0t,y=0+0t, z=0+1t$ or, $x=0,y=0, z=t$