XZ Plane
College/University
Definition
Can be found in a 3 dimensional coordinate system. It is the plane formed by the x-axis and the z-axis. It has the standard equation of y = 0.
Worked examples
\((3, 0, -2)\)
This point lies on the XZ plane because its y-coordinate is zero.
\(y = 0\)
The equation of the XZ plane; every point satisfying it has y-coordinate equal to zero.
Common mistakes
- \((2, 3, 5)\) is on the XZ plane → \((2, 0, 5)\) is on the XZ plane The XZ plane requires y = 0; any point with a nonzero y-coordinate is not on the plane.
- The XZ plane is formed by the x-axis and y-axis → The XZ plane is formed by the x-axis and z-axis The XZ plane uses the x and z axes; the x and y axes form the XY plane.
- The equation of the XZ plane is \(z = 0\) → The equation of the XZ plane is \(y = 0\) Setting y to zero eliminates the y-dimension, leaving only x and z to vary.
Where you'll use it next
You'll use the XZ plane when graphing 3D surfaces and solids, finding intersections of planes in multivariable calculus, and analyzing cross-sections in physics and engineering applications.
Found in 1 StudyPug lesson
Mastering 3D Coordinate Systems: Navigate the Third Dimension
UniversityUniversityMultivariable Calculus
Unlock the power of 3D coordinate systems! Learn to visualize points, planes, and shapes in three dimensions. Discover real-world applications in physics, engineering, and computer graphics.
See also
Reviewed by Pat Cheng, M.Ed. — StudyPug Curriculum Lead · Last updated June 6, 2026