define a line is how to name the intersection of a line and a plane.
define a line is how to name the intersection of a line and a plane.
how to name the intersection of a line and a plane?
define a line
line–plane intersection









































in analytic geometry, the intersection of a line and a plane in three-dimensional space can be the empty set, a point, or a line. it is the entire line if that line is embedded in the plane, and is the empty set if the line is parallel to the plane but outside it. otherwise, the line cuts through the plane at a single point.









































distinguishing these cases, and determining equations for the point and line in the latter cases, have use in computer graphics, motion planning, and collision detection.









































section::::algebraic form.
line–plane intersection
the second approach involves the determination of a point on the mohr circle called the "pole" or the "origin of planes". any straight line drawn from the pole will intersect the mohr circle at a point that represents the state of stress on a plane inclined at the same orientation (parallel) in space as that line. therefore, knowing the stress components formula_137 and formula_138 on any particular plane, one can draw a line parallel to that plane through the particular coordinates formula_1 and formula_2 on the mohr circle and find the pole as the intersection of such line with the mohr circle. as an example, let's assume we have a state of stress with stress components formula_141, formula_142, and formula_143, as shown on figure 7. first, we can draw a line from point formula_81 parallel to the plane of action of formula_12, or, if we choose otherwise, a line from point formula_80 parallel to the plane of action of formula_13. the intersection of any of these two lines with the mohr circle is the pole. once the pole has been determined, to find the state of stress on a plane making an angle formula_148 with the vertical, or in other words a plane having its normal vector forming an angle formula_24 with the horizontal plane, then we can draw a line from the pole parallel to that plane (see figure 7). the normal and shear stresses on that plane are then the coordinates of the point of intersection between the line and the mohr circle.
mohr's circle