Write the parametric equations of the line that is perpendicular to the $xz$-plane and contains the point $P(2, -3, 4).$

Question

At first I think I was overthinking it.

Since it's perpendicular to the $xz$-plane, I assumed it would be parallel to the $y$-axis, making $m=[0,1,0].$
Which would make the vector equation $$[x,y,z]=[2,-3,4] + t[0,1,0].$$ Then I thought the parametric equation would be

$$\begin{aligned}x=& 2\\ y=&-3 + t\\ z=&4 \end{aligned}$$

To me that doesn't look right.

Answer 1

It is correct, as you can check with GeoGebra: