can someone explain why when z=0 , n =k https://www.flickr.com/photos/123101...3/14096908607/
How much do you know about vector geometry?
Do you know that $\vec{i}=<1,0,0>,~\vec{j}=<0,1,0>,~\&~\vec{k}=<0,0 ,1>,$ is the basics for vector spaces.
$\vec{i}$ is the normal for the $yz$-plane; $\vec{j}$ is the normal for the $xz$-plane; $\vec{k}$ is the normal for the $xy$-plane.
It seems to me that you are very confused about all of this material.
Is this an online course?
If you are still confused, perhaps this will help. The coefficients for and are both zero. So, the plane is the same as
So, the normal is:
You find the normal for that plane just as you would find the normal for any other plane.