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y-z Plane

y-z Plane

The plane formed by the y-axis and the z-axis.

 

 

See also

x-y plane, x-z plane

Key Formula

x=0x = 0
Where:
  • xx = The x-coordinate of any point on the y-z plane, which is always zero

Worked Example

Problem: Determine whether each of the following points lies on the y-z plane: A = (0, 3, 5), B = (2, 4, 1), and C = (0, −7, 0).
Step 1: Recall the rule: a point lies on the y-z plane if and only if its x-coordinate equals zero.
x=0x = 0
Step 2: Check point A = (0, 3, 5). The x-coordinate is 0, so A lies on the y-z plane.
A=(0, 3, 5)⇒x=0  ✓A = (0,\, 3,\, 5) \quad \Rightarrow \quad x = 0 \; \checkmark
Step 3: Check point B = (2, 4, 1). The x-coordinate is 2, which is not zero, so B does not lie on the y-z plane.
B=(2, 4, 1)⇒x=2≠0B = (2,\, 4,\, 1) \quad \Rightarrow \quad x = 2 \neq 0
Step 4: Check point C = (0, −7, 0). The x-coordinate is 0, so C lies on the y-z plane. Note that the y or z values do not need to be nonzero.
C=(0, −7, 0)⇒x=0  ✓C = (0,\, -7,\, 0) \quad \Rightarrow \quad x = 0 \; \checkmark
Answer: Points A and C lie on the y-z plane. Point B does not.

Frequently Asked Questions

What is the equation of the y-z plane?
The equation of the y-z plane is simply x = 0. Any point (x, y, z) that satisfies this equation — meaning its first coordinate is zero — lies on the y-z plane, regardless of the values of y and z.
What does the y-z plane look like in 3D?
Picture a flat wall standing straight up and running left-right and up-down at the origin. It extends infinitely in the y-direction (horizontal within the wall) and the z-direction (vertical). It has no thickness in the x-direction. In a standard right-hand coordinate system, the y-z plane is the vertical wall you would face if you looked along the positive x-axis.

y-z plane vs. x-y plane

The y-z plane is defined by x = 0 and contains the y-axis and z-axis. The x-y plane is defined by z = 0 and contains the x-axis and y-axis. Each coordinate plane is named after the two axes it contains, and its equation sets the remaining coordinate to zero. The third coordinate plane, the x-z plane, is defined by y = 0.

Why It Matters

The three coordinate planes (x-y, x-z, and y-z) divide three-dimensional space into eight regions called octants, much like the axes divide 2D space into four quadrants. The y-z plane in particular serves as the boundary where x changes sign, which is important when analyzing symmetry, reflections, and cross-sections. In physics and engineering, projecting a 3D object onto the y-z plane lets you study its profile as seen from the x-direction.

Common Mistakes

Mistake: Setting y = 0 or z = 0 instead of x = 0 when writing the equation of the y-z plane.
Correction: The coordinate that equals zero is the one not in the plane's name. The y-z plane contains the y- and z-axes, so the missing axis is x, giving x = 0.
Mistake: Thinking a point must have nonzero y and z values to be on the y-z plane.
Correction: Any point with x = 0 is on the y-z plane, including points like (0, 0, 0) or (0, 5, 0). The y and z values can be anything, including zero.

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