Answer
$x=1,y=1, z=1+t$
Work Step by Step
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, $x=1,y=1, z=1+t$
