When we say a line lies in a plane, it means that every point on the line is also on the plane. In other words, the line and the plane share at least one common point.
To determine if a line lies in a plane, you can use the slope-intercept form of the line and the general equation of the plane. If the values of x, y, and z in the slope-intercept form satisfy the general equation of the plane, then the line lies in the plane.
Yes, a line can lie in more than one plane. If two or more planes intersect at a line, then that line lies in all of those planes. However, if two planes are parallel, then a line can only lie in one of them.
A line and a plane are both mathematical concepts used to represent points, lines, and shapes in space. A line can lie on a plane, but a plane cannot lie on a line. They are considered to be parallel if they do not intersect.
The concept of a line lying in a plane is used in various real-world situations, such as in architecture, engineering, and navigation. For example, architects use this concept to ensure that walls and floors are properly aligned, while engineers use it to design and construct structures that are stable and structurally sound.