Question

find the parametric equation of the line perpendicular to the xoy plan and through (3, 2, -1)

Answer 1

there are many ways you can write the line. One particular way is to use the vector <0,0,1> as the direction vector of the line.

So r(t) = t<0,0,1> + <3,2-1>

Answer 2

the will gives
x = 3
y = 2
z = t - 1

Answer 3

is <0,0,1> perpendicular to the plane?

Answer 4

yes the vector <0,0,1> is perpendicular to the plane xy

Answer 5

would this make sense?

<x,y,z> = <3,2,-1> + t<0,0,1>

Answer 6

yes