Practice Plane in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Worksheet PDF Free Answer-key PDF Family

Quick Recap

A perfectly flat surface extending infinitely in all directions with zero thickness; defined by three non-collinear points.

An infinite sheet of paper with absolutely no thickness, extending forever in every direction.

Showing a random 20 of 50 problems.

Example 1

medium
Does the line {(t,2t,3t):t∈R}\{(t, 2t, 3t) : t \in \mathbb{R}\} lie in the plane x+y−z=0x + y - z = 0?

Example 2

easy
Two distinct planes in 3D either are parallel or meet in what?

Example 3

medium
How many planes can contain a single given line?

Example 4

medium
In the plane equation 2x+3y+z=62x + 3y + z = 6, find the point where the plane crosses the zz-axis.

Example 5

hard
Find the distance from the origin to the plane 3x−4y+12z=263x - 4y + 12z = 26.

Example 6

hard
Find the equation of the plane that contains the point (1,1,1)(1, 1, 1) and the line {(t,2t,3t)}\{(t, 2t, 3t)\}.

Example 7

easy
A flat floor is a model of which geometric object?

Example 8

medium
True or false: three non-collinear points always determine a unique plane.

Example 9

medium
Two planes are both perpendicular to the same line. How are the two planes related?

Example 10

easy
Two distinct planes intersect. What shape is their intersection?

Example 11

easy
Three points are all on the same line. Do they determine a unique plane?

Example 12

challenge
Three planes pairwise intersect in three different lines, and no two planes are parallel. Describe the possible ways the three planes can meet.

Example 13

hard
Find the angle (in degrees) between the planes x+y=2x + y = 2 and y+z=3y + z = 3.

Example 14

medium
Find the distance from the point (1,2,3)(1, 2, 3) to the plane x+2y+2z=3x + 2y + 2z = 3.

Example 15

easy
A normal vector to the plane 2x−3y+4z=52x - 3y + 4z = 5 is what?

Example 16

easy
How many non-collinear points are needed to determine a unique plane?

Example 17

challenge
How many distinct planes are determined by 4 points in space, no three of which are collinear and not all four coplanar?

Example 18

easy
What is the equation of the xzxz-plane in 3D space?

Example 19

easy
How many dimensions does a plane have, and how many coordinates are needed to specify a point on a plane?

Example 20

medium
Can two distinct planes intersect in exactly one point?
← Back to Plane Worked Examples Formula Explained

Related Concepts

LineDimension