## Thomas' Calculus 13th Edition

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