3d Coordinate System

A Cartesian coordinate system, otherwise known as the 3D coordinate system, is a method employed to pinpoint specific locations within a three-dimensional space. This is accomplished using a trio of values, commonly marked as (x, y, z). Each of these values represents the distance from the origin, measured along the corresponding axis: x-axis (horizontal), y-axis (vertical), and z-axis (depth).

Finding the Distance

Find the distance between the points P(1,2,3) and Q(4,5,6) in 3d space.

More examples

Finding the Plane Parallel to a Line Given four 3d Points

Find the equation of the plane that is parallel to the line of intersection of the planes with equations

2 x - 3 y + z = 5

and

x + y - z = 2

, and passes through the points A(1,2,3), B(2,-1,1), C(-1,2,2) and D(0,1,-1).

More examples

Finding the Intersection of the Line Perpendicular to Plane 1 Through the Origin and Plane 2

Given two planes in 3D space, Plane 1:

3 x - 4 y + 2 z = 12

and Plane 2:

x + 2 y - z = 5

. Find the intersection of the line that passes through the origin and is perpendicular to Plane 1 with Plane 2.

More examples

Finding the Equation of Variation

Find the equation of variation for a point P (x, y, z) that moves so that it is always equidistant from the points A(1, 2, 3) and B(4, 6, 8)

More examples

3d Coordinate System

Finding the Distance

Finding the Plane Parallel to a Line Given four 3d Points

Finding the Intersection of the Line Perpendicular to Plane 1 Through the Origin and Plane 2

Finding the Equation of Variation

Popular Problems