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: If we have the information about the following elements, then we can determine the angle between a line and the plane using the formula below: This phenomenon is shown in the figure below as it shows the angle between a line r and a plane. In other words, we can say that the angle between a straight line and a plane is an angle formed between the line and its orthogonal projection on the plane. This angle that is formed between the line and a plane is actually the angle formed by the straight line with its orthogonal projection on the plane.
There can be the following three scenarios when a straight line and the plane can exist together:
This angle between a line and a plane is equal to the complement of an angle between the normal and the line.
For example, if you draw something on a flat paper, then it means that you are drawing something on a plane.Īn angle between a line and a plane is formed when a line is inclined on a plane, and a normal is drawn to the plane from a point where it is touched by the line. It is also a 2-D figure because like a straight line, it does not have any thickness, rather it has only length and width. A plane is a flat surface that is formed when an infinite number of points extend without limits in any direction.
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