Multivariable calculus and vector analysis

Distance from point to plane example

Example

Find the distance from the point P = (4,-4, 3) to the plane 2x- 2y + 5z + 8 = 0. (This is pictured in the distance to plane CVT in its original view, which you can restore by pressing Home).

Solution: We use formula (2) from the distance to plane reading. From the equation for the plane we substitute A = 2, B = -2, C = 5, D = 8. From the point P, we substitute x₁ = 4, y₁ = -4, and z₁ = 3. The distance from P to the plane is

d = = ≈ 6.8

Contents by topic

1. Geometry in higher dimensions

1a. Preliminaries

1b. Lines and planes

• Parametrization of a line
• Forming planes
• A line or a plane or a point?
• Parametrization of a plane
• Distance from point to plane
• Parametrization of a line examples
• Forming plane examples
• Plane parametrization example
• Distance from point to plane example
• Intersecting planes example

1c. Matrices

1d. Visualizing functions in higher dimensions

2. Differential Calculus

3. Integral calculus

4. Vector calculus

5. The fundamental theorems of vector calculus

6. Review material