Angle Between Line and Plane

The angle between a line, r, and a plane, π, is the angle between r and its orthogonal projection onto π, r'.

Angle Between Line and Plane

The angle between a line and a plane is equal to the complementary acute angle that forms between the direction vector of the line and the normal vector of the plane.

Vectors

Angle Between Line And Plane Example

Angle Between Line And Plane Solution

If the line, r, and the plane, π, are perpendicular, the direction vector of the line and the normal vector of the plane have the same direction and therefore its components are proportional:

Proportional Components

Examples

1. Determine the angle between the line Angle Between Line and Plane Example and the plane Angle Between Line and Plane Example.

Vectors

Angle Between Line And Plane Calculations

Angle Between Line and Plane Solution


2. Determine the angle between the line Angle Between Line and Plane Example and the planeAngle Between Line and Plane Example.

Direction Vector

Vectors

Angle Between Line And Plane Calculations

Angle Solution


3. Determine the angle between the line and the plane:

Angle Between Line and Plane Example

Angle Between Line And Plane Calculations

Angle Between Line And Plane Calculations

Angle Solution