The basis for a plane perpendicular to a line is the fact that a plane and a line are considered perpendicular if they intersect at a 90-degree angle. This means that the direction of the plane's normal vector is perpendicular to the direction of the line.
To find the normal vector of a plane perpendicular to a line, you can use the cross product of any two non-parallel vectors that lie on the plane. Another method is to use the direction vector of the line and any other vector that is perpendicular to it.
Yes, a plane can be perpendicular to more than one line. This occurs when the lines are parallel to each other and lie on the same plane. In this case, the normal vector of the plane will be perpendicular to both lines.
No, a plane perpendicular to a line is not always parallel to another line. The only case where this is true is when the two lines are parallel to each other. In all other cases, the plane and the line will intersect at a 90-degree angle, but they will not be parallel.
The concept of a plane perpendicular to a line is used in many real-life applications, such as architecture and engineering. It is used to create right angles and ensure structural stability in buildings and other structures. It is also used in the design of roads, bridges, and other transportation systems to ensure safe and efficient travel.