Answer
$x=1,y=1, z=1+t$
Work Step by Step
The parametric equations of a straight line can be found by knowing the value of a vector, such as $v=v_1i+v_2j+v_3k$, passing through a point $P(x_0,y_0,z_0)$ as follows:
$x=x_0+t v_1,y=y_0+t v_2; z=z_0+t v_3$
Here, we have the vector $v=\lt 0,0,1 \gt$ that lies on the z-axis.
Thus, we get the parametric equations:
$x=1+0t=1,y=1+0t=1, z=1+t$
or, $x=1,y=1, z=1+t$
