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 \(2x - 3y + z = 5\) 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: \(3x - 4y + 2z = 12\) and Plane 2: \(x + 2y - z = 5\). 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

Popular Problems

Compute $\int_{0}^{\ln (2) / … Solve the triangle. \[ \mathr… QUESTION 2 - 1 POINT Solve th… 5. Suppose you are a computer… Answer the statistical measur… $(-\infty, 2) \cap(-6, \infty… A firm does not pay a dividen… Math 112 Section: 4. Tubercul… Find $y^{\prime}$ if $y=\ln \… 3. (3pts) Cherry trees in a c… More