YZ Plane

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Definition

A part of the three dimensional coordinate system. It is the plane formed by the y-axis and the z-axis. It has the standard equation of x = 0.

Worked examples

\((0, 2, 5)\), \((0, -3, 1)\), \((0, 0, 4)\)

All points on the YZ plane have \(x = 0\); only the y and z coordinates vary.

\(x = 0\)

The equation of the YZ plane; any point satisfying this lies on the plane.

Common mistakes

\((2, 0, 0)\) is on the YZ plane → \((0, 2, 5)\) is on the YZ plane The YZ plane requires \(x = 0\), not \(y = 0\) or \(z = 0\).
The YZ plane has equation \(y = 0\) or \(z = 0\) → The YZ plane has equation \(x = 0\) It is formed by the y and z axes, so the x-coordinate must be zero.
The YZ plane is vertical in standard orientation → The YZ plane is vertical, perpendicular to the x-axis It stands upright when the x-axis points forward; all points on it have the same x-value of zero.

Where you'll use it next

You'll use the YZ plane when graphing 3D surfaces, finding intercepts of planes and solids, setting up triple integrals in calculus, and analyzing symmetry in multivariable functions.

Found in 1 StudyPug lesson

Mastering 3D Coordinate Systems: Navigate the Third Dimension

Multivariable 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.

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