Where does the plane x-y+4z=4 intersect the xy,xz and yz planes? Also, what is the parametric equation of a line perpendicular to this plane going through(3,4,8)?

Question

turingtest · Answer

to find the intersections of each plane let z=0, y=0, and x=0 respectively

turingtest · Answer

the normal vector to the plane is given by$$\vec n=\nabla f(x,y,z)$$

anonymous · Answer

But if I plug in x=0, then I'll have one equation with two variables of y and z...

turingtest · Answer

yes, because the intersection is a line

anonymous · Answer

Ooh I think I got it, I just had to set that into the parametrics and use the "t" value to find the other values. Thanks!

turingtest · Answer

welcome