Question

Find the vector equation of the line through the point p=(0,0,1) and parallel to the y-axis.

Answer 1

The vector that is parallel to the y axis is <0,1,0>. Basically it's the unit vector j that points in the positive y axis direction

\[\Large \vec{r} = \vec{r_0}+t \vec{v}\]

\[\Large \vec{r} = <0,0,1>+t <0,1,0>\]

\[\Large \vec{r} = <0,0,1>+<t*0,t*1,t*0>\]

I'll let you finish