Question

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)?

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

yes, because the intersection is a line

Answer 5

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!

Answer 6

welcome