Is the Tangent Plane Parallel to the Plane?

Well tangent planes to a surface are planes that just touch the surface at the point and are “parallel” to the surface at the point. Note that this gives us a point that is on the plane.

What is parallel to plane?

In geometry, parallel lines are lines in a plane which do not meet; that is, two straight lines in a plane that do not intersect at any point are said to be parallel. ... Parallel planes are planes in the same three-dimensional space that never meet.

At what point is the tangent plane parallel?

If the tangent plane to the surface defined by f(x,y,z)=0 with f(x,y,z)=x2y+y2x+3x−z at the point P=(x,y,z) is parallel to the xy plane, then its normal line must be parallel to the vector →a=<0,0,1>.